GED Math Linear Equations and Inequalities Quiz

1. Solve for x: 3x + 7 = 22

X = 5

X = 10

X = 3

X = 9

To solve the equation 3x + 7 = 22, first subtract 7 from both sides to get 3x = 15. Then, divide both sides by 3 to isolate x, resulting in x = 5. This shows that when x is 5, the original equation holds true.

Explanation

To solve the equation 3x + 7 = 22, first subtract 7 from both sides to get 3x = 15. Then, divide both sides by 3 to isolate x, resulting in x = 5. This shows that when x is 5, the original equation holds true.

2. What is the solution to 2x - 5 = 11?

X = 3

X = 8

X = 6

X = 10

To solve the equation 2x - 5 = 11, first add 5 to both sides, resulting in 2x = 16. Then, divide both sides by 2 to isolate x, yielding x = 8. This demonstrates the correct procedure for solving a linear equation.

Explanation

To solve the equation 2x - 5 = 11, first add 5 to both sides, resulting in 2x = 16. Then, divide both sides by 2 to isolate x, yielding x = 8. This demonstrates the correct procedure for solving a linear equation.

3. Solve: 4x + 3 = 2x + 15

X = 6

X = 4

X = 12

X = 3

To solve the equation 4x + 3 = 2x + 15, first isolate x by subtracting 2x from both sides, yielding 2x + 3 = 15. Then, subtract 3 from both sides to get 2x = 12. Finally, divide by 2 to find x = 6.

Explanation

To solve the equation 4x + 3 = 2x + 15, first isolate x by subtracting 2x from both sides, yielding 2x + 3 = 15. Then, subtract 3 from both sides to get 2x = 12. Finally, divide by 2 to find x = 6.

4. Which value satisfies x + 8 > 15?

X = 5

X = 7

X = 8

X = 10

To satisfy the inequality x + 8 > 15, we can subtract 8 from both sides, resulting in x > 7. Among the given options, x = 10 is the only value that is greater than 7, thus fulfilling the requirement of the inequality.

Explanation

To satisfy the inequality x + 8 > 15, we can subtract 8 from both sides, resulting in x > 7. Among the given options, x = 10 is the only value that is greater than 7, thus fulfilling the requirement of the inequality.

5. Solve the inequality: 3x - 2 < 10

X < 4

X > 4

X < 6

X > 6

To solve the inequality 3x - 2

Explanation

To solve the inequality 3x - 2

6. What is the solution to -2x + 8 = 4?

X = -2

X = 2

X = 6

X = -6

To solve the equation -2x + 8 = 4, first subtract 8 from both sides to get -2x = -4. Then, divide both sides by -2, resulting in x = 2. This shows that when x is 2, the original equation holds true.

Explanation

To solve the equation -2x + 8 = 4, first subtract 8 from both sides to get -2x = -4. Then, divide both sides by -2, resulting in x = 2. This shows that when x is 2, the original equation holds true.

7. Solve: 5(x - 2) = 20

X = 2

X = 6

X = 8

X = 4

To solve the equation 5(x - 2) = 20, first divide both sides by 5, resulting in x - 2 = 4. Then, add 2 to both sides to isolate x, yielding x = 6. This solution satisfies the original equation.

Explanation

To solve the equation 5(x - 2) = 20, first divide both sides by 5, resulting in x - 2 = 4. Then, add 2 to both sides to isolate x, yielding x = 6. This solution satisfies the original equation.

8. Which inequality represents 'a number is at least 12'?

X < 12

X ≤ 12

X ≥ 12

X > 12

The phrase "at least 12" indicates that the number can be equal to 12 or any number greater than 12. Therefore, the inequality that correctly represents this condition is \( x \geq 12 \), meaning \( x \) is greater than or equal to 12.

Explanation

The phrase "at least 12" indicates that the number can be equal to 12 or any number greater than 12. Therefore, the inequality that correctly represents this condition is \( x \geq 12 \), meaning \( x \) is greater than or equal to 12.

9. Solve for y: 2y + 3 = y + 9

Y = 3

Y = 6

Y = 9

Y = 12

To solve for y in the equation 2y + 3 = y + 9, first subtract y from both sides, resulting in y + 3 = 9. Then, subtract 3 from both sides to isolate y, yielding y = 6. Thus, the solution to the equation is y = 6.

Explanation

To solve for y in the equation 2y + 3 = y + 9, first subtract y from both sides, resulting in y + 3 = 9. Then, subtract 3 from both sides to isolate y, yielding y = 6. Thus, the solution to the equation is y = 6.

10. Solve the inequality: -x + 5 ≥ 2

X ≤ 3

X ≥ 3

X < 7

X > 7

To solve the inequality -x + 5 ≥ 2, first isolate x by subtracting 5 from both sides, resulting in -x ≥ -3. Multiplying through by -1 reverses the inequality, giving x ≤ 3. Thus, the solution indicates that x can take any value less than or equal to 3.

Explanation

To solve the inequality -x + 5 ≥ 2, first isolate x by subtracting 5 from both sides, resulting in -x ≥ -3. Multiplying through by -1 reverses the inequality, giving x ≤ 3. Thus, the solution indicates that x can take any value less than or equal to 3.

11. What is the solution to (x/2) + 3 = 8?

X = 5

X = 10

X = 15

X = 20

To solve the equation (x/2) + 3 = 8, first subtract 3 from both sides to get (x/2) = 5. Then, multiply both sides by 2 to isolate x, resulting in x = 10. This shows that x equals 10 satisfies the original equation.

Explanation

To solve the equation (x/2) + 3 = 8, first subtract 3 from both sides to get (x/2) = 5. Then, multiply both sides by 2 to isolate x, resulting in x = 10. This shows that x equals 10 satisfies the original equation.

12. Solve: 6x - 4 = 2x + 12

X = 2

X = 4

X = 8

X = 10

To solve the equation 6x - 4 = 2x + 12, first, isolate the variable x by moving all terms involving x to one side and constant terms to the other. Simplifying the equation leads to 4x = 16, which gives x = 4. Thus, the solution to the equation is x = 4.

Explanation

To solve the equation 6x - 4 = 2x + 12, first, isolate the variable x by moving all terms involving x to one side and constant terms to the other. Simplifying the equation leads to 4x = 16, which gives x = 4. Thus, the solution to the equation is x = 4.