Q. If 3 times a number plus 4 equals 19, what is the number?
Solution
Let the number be x. The equation is 3x + 4 = 19. Subtracting 4 from both sides gives 3x = 15. Dividing by 3 gives x = 5.
Correct Answer:
B
— 5
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Q. If 3(x + 2) < 2(x + 5), what is the value of x?
-
A.
x < 1
-
B.
x > 1
-
C.
x = 1
-
D.
x = 0
Solution
Step 1: Distribute: 3x + 6 < 2x + 10. Step 2: Subtract 2x from both sides: x + 6 < 10. Step 3: Subtract 6: x < 4.
Correct Answer:
A
— x < 1
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Q. If 3(x - 1) < 2x + 4, what is the solution for x?
-
A.
x < 7
-
B.
x > 7
-
C.
x < 5
-
D.
x > 5
Solution
Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.
Correct Answer:
C
— x < 5
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Q. If 3(x - 1) < 2x + 4, what is the value of x?
-
A.
x < 7
-
B.
x > 7
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.
Correct Answer:
A
— x < 7
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Q. If 3(x - 2) = 12, what is x?
-
A.
x = 4
-
B.
x = 6
-
C.
x = 8
-
D.
x = 10
Solution
Step 1: Divide both sides by 3: x - 2 = 4. Step 2: Add 2 to both sides: x = 6.
Correct Answer:
B
— x = 6
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Q. If 3(x - 4) = 9, what is x?
-
A.
x = 1
-
B.
x = 4
-
C.
x = 7
-
D.
x = 10
Solution
Step 1: Divide both sides by 3: x - 4 = 3. Step 2: Add 4 to both sides: x = 7.
Correct Answer:
C
— x = 7
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Q. If 3x + 2 < 5, what is the value of x?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 2 from both sides: 3x < 3. Step 2: Divide by 3: x < 1.
Correct Answer:
A
— x < 1
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Q. If 3x + 4 < 2x + 10, what is the value of x?
-
A.
x < 6
-
B.
x > 6
-
C.
x < 2
-
D.
x > 2
Solution
Step 1: Subtract 2x from both sides: x + 4 < 10. Step 2: Subtract 4: x < 6.
Correct Answer:
A
— x < 6
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Q. If 3x + 4 = 19, what is x?
-
A.
x = 3
-
B.
x = 5
-
C.
x = 4
-
D.
x = 6
Solution
Subtract 4 from both sides: 3x = 15. Divide by 3: x = 5.
Correct Answer:
B
— x = 5
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Q. If 4 times a number decreased by 2 equals 10, what is the number?
Solution
Let the number be x. The equation is 4x - 2 = 10. Adding 2 to both sides gives 4x = 12. Dividing by 4 gives x = 3.
Correct Answer:
C
— 4
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Q. If 4 times a number is increased by 6, the result is 30. What is the number?
Solution
Let the number be x. Then, 4x + 6 = 30. Subtracting 6 from both sides gives 4x = 24. Dividing by 4 gives x = 6.
Correct Answer:
B
— 7
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Q. If 4x + 1 = 2x + 9, what is x?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 5
Solution
Step 1: Subtract 2x from both sides: 2x + 1 = 9. Step 2: Subtract 1 from both sides: 2x = 8. Step 3: Divide by 2: x = 4.
Correct Answer:
B
— x = 3
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Q. If 4x + 5 = 29, what is the value of x?
Solution
Subtract 5 from both sides: 4x = 24. Divide by 4: x = 6.
Correct Answer:
C
— 6
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Q. If 4x - 1 < 3x + 2, what is the value of x?
-
A.
x < 3
-
B.
x > 3
-
C.
x < 1
-
D.
x > 1
Solution
Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.
Correct Answer:
A
— x < 3
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Q. If 4x - 7 < 9, what is the maximum value of x?
Solution
Step 1: Add 7 to both sides: 4x < 16. Step 2: Divide by 4: x < 4.
Correct Answer:
B
— 3
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Q. If 5 times a number decreased by 3 equals 12, what is the number?
Solution
Let the number be x. The equation is: 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.
Correct Answer:
C
— 4
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Q. If 5 times a number is decreased by 2, the result is 18. What is the number?
Solution
Let the number be x. Then, 5x - 2 = 18. Adding 2 to both sides gives 5x = 20. Dividing by 5 gives x = 4.
Correct Answer:
C
— 6
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Q. If 5(x - 1) = 15, what is x?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 5
Solution
Step 1: Divide both sides by 5: x - 1 = 3. Step 2: Add 1 to both sides: x = 4.
Correct Answer:
D
— x = 5
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Q. If 5(x - 1) = 20, what is x?
-
A.
x = 3
-
B.
x = 4
-
C.
x = 5
-
D.
x = 6
Solution
Step 1: Divide both sides by 5: x - 1 = 4. Step 2: Add 1 to both sides: x = 5.
Correct Answer:
D
— x = 6
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Q. If 5x + 2 > 12, what is the smallest integer value of x?
Solution
Subtract 2 from both sides: 5x > 10. Then divide by 5: x > 2.
Correct Answer:
C
— 3
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Q. If 5x + 2 < 17, what is the largest integer value of x?
Solution
Subtract 2: 5x < 15. Divide by 5: x < 3. The largest integer is 2.
Correct Answer:
C
— 4
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Q. If 5x + 2 = 3x + 10, what is the value of x?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 4
Solution
Subtract 3x from both sides: 2x + 2 = 10. Then subtract 2: 2x = 8. Finally, divide by 2: x = 4.
Correct Answer:
B
— x = 2
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Q. If 5x + 2y = 20 and y = 2, what is the value of x?
Solution
Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.
Correct Answer:
C
— 4
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Q. If 5x - 2 > 3x + 6, what is the value of x?
-
A.
x < 4
-
B.
x > 4
-
C.
x = 4
-
D.
x = 3
Solution
Step 1: Subtract 3x from both sides: 2x - 2 > 6. Step 2: Add 2: 2x > 8. Step 3: Divide by 2: x > 4.
Correct Answer:
B
— x > 4
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Q. If 5x - 2 ≤ 3, what is the maximum value of x?
-
A.
x ≤ 1
-
B.
x ≤ 2
-
C.
x ≤ 3
-
D.
x ≤ 4
Solution
Step 1: Add 2 to both sides: 5x ≤ 5. Step 2: Divide by 5: x ≤ 1.
Correct Answer:
A
— x ≤ 1
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Q. If 6x - 3 = 3x + 12, what is the value of x?
Solution
Subtract 3x from both sides: 3x - 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5.
Correct Answer:
B
— 4
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Q. If 6x - 4 = 26, what is x?
-
A.
x = 4
-
B.
x = 5
-
C.
x = 6
-
D.
x = 7
Solution
Step 1: Add 4 to both sides: 6x = 30. Step 2: Divide both sides by 6: x = 5.
Correct Answer:
B
— x = 5
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Q. If 7x - 3 = 4x + 6, what is x?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 4
Solution
Subtract 4x from both sides: 3x - 3 = 6. Add 3: 3x = 9. Divide by 3: x = 3.
Correct Answer:
B
— x = 2
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Q. If 8 - 2x = 0, what is x?
-
A.
x = 2
-
B.
x = 3
-
C.
x = 4
-
D.
x = 5
Solution
Step 1: Subtract 8 from both sides: -2x = -8. Step 2: Divide by -2: x = 4.
Correct Answer:
A
— x = 2
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Q. If 8 - 3x = 2, what is x?
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 4
Solution
Step 1: Subtract 8 from both sides: -3x = -6. Step 2: Divide both sides by -3: x = 2.
Correct Answer:
A
— x = 1
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