Interactive multiple-choice quiz: Solving Linear Equations Practice ريفيل
This document provides examples and exercises for solving one-step linear equations involving addition and subtraction. It includes problems with fractions, identification of equality properties, and real-world word problem applications.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
بعض الأسئلة غير مكتملة الإعداد
يوجد سؤال واحد على الأقل لا يحتوي على إجابة صحيحة صالحة في الحقل r_a، لذلك قد لا يعمل التصحيح الفوري بشكل كامل في جميع الأسئلة.
Question 1
Points: 10
Write an equation for the sentence: Four times a number less 10 is equal to 16.
Explanation
Four times x is 4x, and 10 less gives 4x - 10.
Question 2
Points: 10
Etu has read 12 of the 32 chapters in his assigned book. He plans to finish the book by reading c chapters each day for 8 days. Which equation best represents the situation?
Explanation
The 12 chapters already read plus 8 days of c chapters per day equals 32.
Question 3
Points: 10
MOTORS: The horsepower H of a motor is the product of motor speed M and torque T divided by 5252. Translate the sentence into a formula.
Explanation
The product MT is divided by 5252, so H = MT/5252.
Question 4
Points: 10
Write a sentence for the equation 6z - 15 = 45.
Explanation
The equation first multiplies z by 6 and then subtracts 15.
Question 5
Points: 10
Write a sentence for the equation (y + 3)2 = 25.
Explanation
Parentheses show that the entire quantity y + 3 is squared.
Question 6
Points: 10
Select all statements that represent 7(p + 23) = 102. A: Seven times the sum of p and twenty-three is the same as one hundred two. B: Seven times p plus twenty-three equals one hundred two. C: Seven times the quantity p plus twenty-three equals one hundred two. D: The quantity seven times p plus twenty-three is the same as one hundred two. E: Seven times the sum of p and twenty-three is one hundred two.
Explanation
Statements A, C, and E all apply the factor 7 to the entire quantity p + 23.
Question 7
Points: 10
The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c. Which formula represents this statement?
Explanation
A triangle perimeter is the sum of its three side lengths.
Question 8
Points: 10
Write a sentence for the equation 4m = 52.
Explanation
The expression 4m means four times m.
Question 9
Points: 10
What is the verbal sentence for the equation 7(p + 23) = 102?
Explanation
Parentheses make p + 23 a sum that is multiplied by 7.
Question 10
Points: 10
Write a sentence for the equation r2 - 15 = t + 19.
Explanation
The exponent 2 applies to r, followed by subtracting 15.
Question 11
Points: 10
Solve 2/3 + w = 1 1/2. State which property of equality you used.
Explanation
Subtract 2/3 from both sides: w = 3/2 - 2/3 = 5/6.
Question 12
Points: 10
Solve the equation a + 26 = 35.
Explanation
Subtract 26 from both sides to get a = 9.
Question 13
Points: 10
On average, a male bulldog weighs 15 pounds less than a male golden retriever. If the average male bulldog weighs 50 pounds, write and solve an equation for the average weight w of a male golden retriever.
Explanation
A bulldog is 15 pounds lighter, so 50 = w - 15 and w = 65.
Question 14
Points: 10
Solve the equation 6y = 54.
Explanation
Divide both sides by 6 to get y = 9.
Question 15
Points: 10
Solve the equation v - 9 = 14.
Explanation
Add 9 to both sides to get v = 23.
Question 16
Points: 10
Solve the equation 44 = t - 72.
Explanation
Add 72 to both sides: t = 44 + 72 = 116.
Question 17
Points: 10
Solve the equation -61 = d + (-18).
Explanation
Add 18 to both sides: d = -61 + 18 = -43.
Question 18
Points: 10
Solve the equation 18 + z = 40.
Explanation
Subtract 18 from both sides to get z = 22.
Question 19
Points: 10
Solve the equation -4a = 48.
Explanation
Divide both sides by -4 to get a = -12.
Question 20
Points: 10
Write an equation for the sentence and solve it: Six times a number is 132. Let n be the number.
Explanation
Six times n is 6n, and 132 divided by 6 is 22.
Question 21
Points: 10
Write an equation for the sentence and solve it: Two thirds equals negative eight times a number. Let n be the number.
Explanation
Divide 2/3 by -8 to get n = -1/12.
Question 22
Points: 10
Solve the equation 3m + 4 = -11.
Explanation
Subtract 4 and divide by 3: m = -15/3 = -5.
Question 23
Points: 10
Solve the equation 8 = (x - 5)/7.
Explanation
Multiply by 7 to get 56 = x - 5, then add 5: x = 61.
Question 24
Points: 10
A sporting goods store sold 2/3 of its basketballs, but 8 were returned. Now the store has 38 basketballs. How many were there originally? Let b be the original number.
Explanation
After selling 2/3, the store has 1/3 of b left. Thus (1/3)b + 8 = 38 and b = 90. The source PDF incorrectly prints 2/3 in the intended correct choice, so that fraction is corrected here.
Question 25
Points: 10
Solve 2 - ax = -8 for x. Assume a ≠ 0.
Explanation
Subtract 2 to get -ax = -10, then divide by -a: x = 10/a.
Question 26
Points: 10
Use properties of equality to solve 3t + 7 = -8. Check your solution.
Explanation
Subtract 7 and divide by 3: t = -15/3 = -5.
Question 27
Points: 10
Use properties of equality to solve 8 = 16 + 8n. Check your solution.
Explanation
Subtract 16 to get -8 = 8n, so n = -1.
Question 28
Points: 10
Use properties of equality to solve -34 = 6m - 4. Check your solution.
Explanation
Add 4 to get -30 = 6m, so m = -5.
Question 29
Points: 10
Use properties of equality to solve 9x + 27 = -72. Check your solution.
Explanation
Subtract 27 and divide by 9: x = -99/9 = -11.
Question 30
Points: 10
Use properties of equality to solve f/(-7) - 8 = 2. Check your solution.
Explanation
Add 8 to get f/(-7) = 10, so f = -70.
Question 31
Points: 10
Use properties of equality to solve 1 + r/9 = 4. Check your solution.
Explanation
Subtract 1 to get r/9 = 3, so r = 27.
Question 32
Points: 10
Use properties of equality to solve k/3 + 4 = -16. Check your solution.
Explanation
Subtract 4 to get k/3 = -20, so k = -60.
Question 33
Points: 10
Use properties of equality to solve (n - 2)/7 = 2. Check your solution.
Explanation
Multiply by 7 and add 2: n - 2 = 14, so n = 16.
Question 34
Points: 10
Use properties of equality to solve 14 = (6 + z)/(-2). Check your solution.
Explanation
Multiply by -2: -28 = 6 + z, so z = -34.
Question 35
Points: 10
Use properties of equality to solve -11 = (a - 5)/6. Check your solution.
Explanation
Multiply by 6: -66 = a - 5, so a = -61.
Question 36
Points: 10
Use properties of equality to solve (22 - w)/3 = -7. Check your solution.
Explanation
Multiply by 3: 22 - w = -21, so -w = -43 and w = 43.
Question 37
Points: 10
Solve the equation 5 + 7a = 4a - 13.
Explanation
Subtract 4a and 5: 3a = -18, so a = -6.
Question 38
Points: 10
BASKETBALL: Last season Nolan scored 750 points in 30 games and Victor scored 782 points in 34 games. Assume they play every game this season and score at the same constant rates as last season. After how many games p will they have the same number of career points?
Explanation
Their rates are 25 and 23 points per game. Solving 25p + 750 = 23p + 782 gives p = 16.
Question 39
Points: 10
Solve the equation 7(n - 2) + 8 = 3(n - 4) - 2.
Explanation
Expand to 7n - 6 = 3n - 14, so 4n = -8 and n = -2.
Question 40
Points: 10
Solve the equation 5y = (12y + 16)/4.
Explanation
The right side is 3y + 4. Thus 5y = 3y + 4 and y = 2.
Question 41
Points: 10
GEOMETRY: A rectangle has width x cm and height 10 cm. A second rectangle has length (x + 3) cm and height 6 cm. Find x so the rectangles have the same area.
Explanation
Set 10x = 6(x + 3). Then 4x = 18, so x = 9/2.
Question 42
Points: 10
Solve the equation 6(y - 5) = 2(10 + 3y).
Explanation
Expansion gives 6y - 30 = 20 + 6y, which reduces to -30 = 20, so there is no solution.
Question 43
Points: 10
Solve 3(2b - 1) - 7 = 6b - 10 and state whether it has one solution, no solution, or is an identity.
Explanation
Both sides simplify to 6b - 10, so the equation is true for every b.
Question 44
Points: 10
Solve the equation 7c + 12 = -4c + 78.
Explanation
Add 4c and subtract 12: 11c = 66, so c = 6.
Question 45
Points: 10
Solve the equation 2m - 13 = -8m + 27.
Explanation
Add 8m and 13: 10m = 40, so m = 4.
Question 46
Points: 10
Solve the equation 9x - 4 = 2x + 3.
Explanation
Subtract 2x and add 4: 7x = 7, so x = 1.
Question 47
Points: 10
A triangle has base 8 and height x + 4. A rectangle has length x + 6 and width 3. Find x so the figures have the same area.
Explanation
Set (1/2)(8)(x + 4) = 3(x + 6). This gives 4x + 16 = 3x + 18, so x = 2.
Question 48
Points: 10
Solve -6y - 3 = 3 - 6y and state whether it has one solution, no solution, or is an identity.
Explanation
Canceling -6y from both sides gives the false statement -3 = 3, so there is no solution.
Question 49
Points: 10
Solve (1/2)(x + 6) = (1/2)x - 9 and state whether it has one solution, no solution, or is an identity.
Explanation
The left side is x/2 + 3. Canceling x/2 gives 3 = -9, so there is no solution.
Question 50
Points: 10
Solve the equation 2x = 2(x - 3).
Explanation
The right side is 2x - 6. Subtracting 2x gives 0 = -6, so there is no solution.
Question 51
Points: 10
Graph the solution set of |2t - 4| = 8.
Explanation
Solve 2t - 4 = 8 or 2t - 4 = -8 to get t = 6 or t = -2.
Question 52
Points: 10
Which statement must be true for the solution of |ax + b| = c to be the empty set?
Explanation
An absolute value cannot equal a negative number, so c must be negative.
Question 53
Points: 10
SKYDIVING: It takes approximately 6 minutes for a skydiver to land after she jumps out of a plane, give or take 30 seconds. What is the range of time, in seconds, it could take?
Explanation
Six minutes is 360 seconds. Thirty seconds less or more gives the interval [330, 390].
Question 54
Points: 10
Label both graphs with equations. Graph 1 has points at -2 and 4. Graph 2 has points at -9 and 3. Use A: |x - 1| = 3, B: |x - 3| = 5, C: |x - 1| = 6, D: |x + 3| = 6.
Explanation
The midpoint and distance are 1 and 3 for Graph 1, and -3 and 6 for Graph 2.
Question 55
Points: 10
Solve |n - 3| = 5 and choose the correct solution set.
Explanation
Set n - 3 equal to 5 and -5 to get n = 8 and n = -2.
Question 56
Points: 10
Solve |f + 10| = 1 and choose the correct solution set.
Explanation
Set f + 10 equal to 1 and -1 to get f = -9 and f = -11.
Question 57
Points: 10
Solve the equation |7 - 2q| = 3.
Explanation
Solve 7 - 2q = 3 and 7 - 2q = -3 to get q = 2 and q = 5.
Question 58
Points: 10
Solve the equation |4x - 2| = 26.
Explanation
Solve 4x - 2 = 26 and 4x - 2 = -26 to get x = 7 and x = -6.
Question 59
Points: 10
Solve the equation |w + 1| = 5.
Explanation
Solve w + 1 = 5 and w + 1 = -5 to get w = 4 and w = -6.
Question 60
Points: 10
Solve the equation |n + 2| = -1.
Explanation
An absolute value cannot be negative, so there is no solution.
Question 61
Points: 10
Solve the equation |m - 2| = 2.
Explanation
Solve m - 2 = 2 and m - 2 = -2 to get m = 4 and m = 0.
Question 62
Points: 10
Solve the equation |(-1/2)b - 2| = 10.
Explanation
Solve (-1/2)b - 2 = 10 and (-1/2)b - 2 = -10 to get b = -24 and b = 16.
Question 63
Points: 10
Solve the equation |-4d + 6| = 12.
Explanation
Solve -4d + 6 = 12 and -4d + 6 = -12 to get d = -3/2 and d = 9/2.
Question 64
Points: 10
Write an equation involving absolute value for the graph.
Question 65
Points: 10
Write an equation involving absolute value for the graph.
Question 66
Points: 10
Solve (n - 4)/8 = 3/2. If necessary, round to the nearest hundredth.
Explanation
Multiply by 8 to get n - 4 = 12, so n = 16.
Question 67
Points: 10
Solve x/12 = (2x - 5)/18. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 18x = 24x - 60, so x = 10.
Question 68
Points: 10
MIXTURE: Oscar makes fruit punch by mixing 8 parts cranberry juice to 3 parts pineapple juice. How many cups of pineapple juice are needed with 48 cups of cranberry juice?
Explanation
Use 8/3 = 48/p. Since 48 is 6 times 8, p = 6 × 3 = 18 cups.
Question 69
Points: 10
Ayita is making 12 gallons of a mixture that is 20% plant food and 80% water. Which proportions can be used to find the amount p of plant food? A: 20/80 = p/12. B: 20/100 = p/12. C: 80/100 = p/12. D: 20/p = 80/12. E: (12 - p)/12 = 80/100. Select all that apply.
Explanation
Plant food is 20% of the total, giving B. Water is 12 - p and 80% of the total, giving E.
Question 70
Points: 10
Solve the proportion 3/8 = 15/a. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 3a = 120, so a = 40.
Question 71
Points: 10
Solve the proportion t/2 = 6/12. If necessary, round to the nearest hundredth.
Explanation
Since 6/12 = 1/2, t/2 = 1/2 and t = 1.
Question 72
Points: 10
Solve the proportion 4/9 = 13/q. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 4q = 117, so q = 29.25.
Question 73
Points: 10
Solve (4v + 7)/15 = (6v + 2)/10. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 40v + 70 = 90v + 30, so 40 = 50v and v = 0.8.
Question 74
Points: 10
Solve (9b - 3)/9 = (5b + 5)/3. If necessary, round to the nearest hundredth.
Explanation
Cross multiply and simplify: 27b - 9 = 45b + 45, so b = -3.
Question 75
Points: 10
Solve (2n - 4)/5 = (3n + 3)/10. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 20n - 40 = 15n + 15, so n = 11.
Question 76
Points: 10
Solve 2/(g + 6) = 4/(5g + 10). If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 10g + 20 = 4g + 24, so g = 2/3 ≈ 0.67.
Question 77
Points: 10
Solve the proportion 9/g = 15/10. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 90 = 15g, so g = 6.
Question 78
Points: 10
Solve the proportion 3/a = 1/6. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: a = 18.
Question 79
Points: 10
Solve the proportion 6/z = 3/5. If necessary, round to the nearest hundredth.
Explanation
Cross multiply: 30 = 3z, so z = 10.
Question 80
Points: 10
Solve the equation 5a - 2b = 15 for a.
Explanation
Add 2b and divide by 5: a = (15 + 2b)/5 = 3 + 2b/5.
Question 81
Points: 10
Solve 2v = (w + v)/t for v.
Explanation
Multiply by t: 2tv = w + v. Then v(2t - 1) = w, so v = w/(2t - 1).
Question 82
Points: 10
The volume of a cylindrical jar is V = πr2h. What formula should be used to find the height h?
Explanation
Divide V = πr2h by πr2 to get h = V/(πr2).
Question 83
Points: 10
A cylindrical jar has radius 1.5 inches and original volume 30 cubic inches. What height should a new jar have to increase the volume by 6 cubic inches?
Explanation
The new volume is 36. Using h = V/(πr2) gives 36/(π × 1.52) ≈ 5.09 inches.
Question 84
Points: 10
VIDEO GAMES: Ella models profit with P = 40c - 300, where c is the number of copies sold. Which equation gives c for a specific profit P?
Explanation
Add 300 and divide by 40: c = (P + 300)/40.
Question 85
Points: 10
COOKING: Adelina needs 96 cloves of garlic. Each bag contains 3 heads, and each head has about 8 cloves. What assumption must she make when calculating how many bags to buy?
Explanation
The number of cloves per head is approximate, so the calculation assumes exactly 8 cloves per head.
Question 86
Points: 10
How many bags of garlic should Adelina purchase if she needs 96 cloves, each bag has 3 heads, and each head has 8 cloves?
Explanation
Each bag contains 3 × 8 = 24 cloves, and 96 ÷ 24 = 4 bags.
Question 87
Points: 10
AGRICULTURE: A dairy cow produces 832 ounces of milk per day. About how many gallons does it produce per year? Use 1 cup = 8 ounces, 1 quart = 4 cups, and 1 gallon = 4 quarts.
Explanation
One gallon is 128 ounces. Thus 832/128 = 6.5 gallons per day, and 6.5 × 365 = 2372.5 gallons per year.
Question 88
Points: 10
Solve the equation x - 2y = 1 for y.
Explanation
Subtract x: -2y = 1 - x. Dividing by -2 gives y = (x - 1)/2.
Question 89
Points: 10
Solve the equation d + 3n = 1 for n.
Explanation
Subtract d and divide by 3: n = (1 - d)/3.
Question 90
Points: 10
Solve the equation u = vw + z for v.
Explanation
Subtract z and divide by w: v = (u - z)/w. The source PDF incorrectly labels the left side of its answer choices as u.
Question 91
Points: 10
Solve the equation x = b - cd for c.
Explanation
Rearrange to cd = b - x, then divide by d: c = (b - x)/d.
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