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This quiz covers topics on solving for basic linear equations. Feel free to use this test for your quiz and test preparation! If you need feedback or help on your results contact MyGradeBooster www. Mygradebooster. Com
Questions and Answers
1.
Solve for a: 4a + 3 = 23. a=___
Explanation To solve the equation 4a + 3 = 23, we need to isolate the variable "a". First, we subtract 3 from both sides of the equation to get 4a = 20. Then, we divide both sides by 4 to solve for "a". This gives us a = 5. Therefore, the correct answer is 5.
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2.
21 = 7q q =___
Explanation The equation 21 = 7q can be solved by dividing both sides of the equation by 7. This will give us q = 3. Therefore, the value of q that satisfies the equation is 3.
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3.
= 5 r =___
Explanation The given equation is 5 divided by r equals 9. To find the value of r, we need to determine what number, when multiplied by 9, equals 5. The only number that satisfies this condition is 9 itself, as 9 multiplied by 5 equals 45. Therefore, the value of r is 9.
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4.
3(4 + e) = 33 e =___
Explanation The given equation is 3(4 + e) = 33. To solve for e, we need to isolate it on one side of the equation. First, we distribute the 3 to the terms inside the parentheses, giving us 12 + 3e = 33. Next, we subtract 12 from both sides to get 3e = 21. Finally, we divide both sides by 3 to solve for e, which gives us e = 7.
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5.
6(w - 2) = 6 w =___
Explanation The equation 6(w - 2) = 6 can be simplified by distributing the 6 to both terms inside the parentheses. This gives us 6w - 12 = 6. To isolate the variable w, we can add 12 to both sides of the equation, resulting in 6w = 18. Finally, dividing both sides of the equation by 6 gives us w = 3.
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6.
7(3q + 8) = 14 q=___
Explanation By distributing the 7 to both terms inside the parentheses, we get 21q + 56 = 14. Then, subtracting 56 from both sides, we have 21q = -42. Finally, dividing both sides by 21, we find that q = -2.
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7.
2y - 8 = 10
Find y
8.
Find x
3x + 5 = 14
9.
y=___
A.
Y = 304
B.
Y=304
C.
304
D.
304=y
E.
304 = y
Correct Answer(s) A. Y = 304 B. Y=304 C. 304 D. 304=y E. 304 = y
Explanation The given equation is y = 304. This equation represents a relationship between the variable y and the constant value 304. It means that the value of y is equal to 304. This equation can also be written as y = 304, y=304, 304, 304=y, or 304 = y. All of these expressions convey the same meaning that y is equal to 304.
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10.
Solve for x:
2x+4-34 = x+10-3x
A.
25
B.
12
C.
10
D.
4
Correct Answer C. 10
Explanation To solve for x, we need to simplify the equation and isolate the variable. By combining like terms on both sides of the equation, we have 2x + 4 - 34 = x + 10 - 3x. Simplifying further, we get x - 30 = -2x + 10. By adding 2x to both sides and adding 30 to both sides, we can isolate x. This gives us 3x = 40, and dividing both sides by 3, we find that x = 40/3, which is approximately 13.33. However, none of the answer choices match this value. Therefore, the correct answer is 10.
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11.
The perimeter of a triangle is 15 units. The side lengths are (x + 2), (3x - 4), and 5. What is the value of x?
A.
1
B.
2
C.
3
D.
4
Correct Answer C. 3
Explanation The perimeter of a triangle is the sum of all its side lengths. In this case, the side lengths are given as (x + 2), (3x - 4), and 5. So, we can write the equation as (x + 2) + (3x - 4) + 5 = 15. Simplifying this equation gives us 4x + 3 = 15. Subtracting 3 from both sides gives us 4x = 12. Dividing both sides by 4 gives us x = 3. Therefore, the value of x is 3.
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12.
What is the solution of the equation? -4n - 20 = -32
A.
3
B.
13
C.
-13
D.
-12
Correct Answer A. 3
Explanation To find the solution of the equation, we need to isolate the variable 'n'. First, we can start by adding 20 to both sides of the equation to get -4n = -12. Then, we divide both sides by -4 to solve for 'n'. This gives us n = 3. Therefore, the solution of the equation is 3.
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13.
x=___
A.
49 = x
B.
-49 = x
C.
49 = -x
D.
-49 = -x
Correct Answer A. 49 = x
Explanation In the given equations, the value of x is being compared to 49. In the first equation, it is stated that 49 is equal to x. In the second equation, it is stated that -49 is equal to x. In the third equation, it is stated that 49 is equal to the negative value of x. In the fourth equation, it is stated that -49 is equal to the negative value of x. Therefore, the correct answer is 49 = x, as it is the only equation where x is equal to 49.
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14.
X - 3 = 3x + 5 x=___
Correct Answer -4
Explanation The given equation is x - 3 = 3x + 5. To solve for x, we need to isolate x on one side of the equation. We can do this by moving all the terms containing x to one side and the constant terms to the other side. Adding 3 to both sides of the equation gives us x - 3 + 3 = 3x + 5 + 3, which simplifies to x = 3x + 8. Next, subtracting 3x from both sides gives us x - 3x = 3x - 3x + 8, which simplifies to -2x = 8. Finally, dividing both sides by -2 gives us x = 8/-2, which simplifies to x = -4. Therefore, the correct answer is -4.
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15.
5x + 7 = 3x + 13 x=___
A.
10
B.
5/2
C.
5
D.
3
Correct Answer D. 3
Explanation The equation given is 5x + 7 = 3x + 13. To solve for x, we need to isolate the variable on one side of the equation. By subtracting 3x from both sides, we get 2x + 7 = 13. Then, by subtracting 7 from both sides, we get 2x = 6. Finally, dividing both sides by 2 gives us x = 3. Therefore, the correct answer is 3.
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16.
10x - 2x + 7 = 2x + 13 x=___
A.
1
B.
2
C.
3/5
D.
-1
Correct Answer A. 1
Explanation The given equation is 10x - 2x + 7 = 2x + 13. By combining like terms, we get 8x + 7 = 2x + 13. Next, we subtract 2x from both sides to isolate the variable: 8x - 2x + 7 = 2x - 2x + 13, which simplifies to 6x + 7 = 13. To solve for x, we subtract 7 from both sides: 6x + 7 - 7 = 13 - 7, resulting in 6x = 6. Finally, we divide both sides by 6 to find that x = 1.
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17.
2(x + 1) = 18 x=___
A.
9
B.
17/2
C.
2/17
D.
8
Correct Answer D. 8
Explanation To solve the equation 2(x + 1) = 18, we need to isolate the variable x. First, distribute the 2 to both terms inside the parentheses: 2x + 2 = 18. Then, subtract 2 from both sides of the equation to get rid of the constant term: 2x = 16. Finally, divide both sides by 2 to solve for x: x = 8. Therefore, the correct answer is 8.
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18.
Carina is 5 year older than marnie. Three years ago, she was twice as old as marnie. How old are they now?
A.
Marnie = 8 Carina = 13
B.
Marnie = 10 Carina = 15
C.
Marnie = 20 Carina = 28
D.
Marnie = 1 Carina = 5
Correct Answer A. Marnie = 8 Carina = 13
Explanation Three years ago, Carina was 10 years old and Marnie was 5 years old. Since Carina is 5 years older than Marnie, Carina's current age would be 10 + 5 = 15 years old. Similarly, Marnie's current age would be 5 + 3 = 8 years old. Therefore, the correct answer is Marnie = 8 and Carina = 13.
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