Algebra Test Inequalities 3

Question 1

Solve: |x| < 4

Accepted Answer

-4 < x < 4

Answer

|x| < 4 means x is within 4 units of zero: -4 < x < 4.

Question 2

Solve: |x - 2| > 3

Accepted Answer

x > 5 or x < -1

Answer

|x - 2| > 3 means x - 2 > 3 or x - 2 < -3, giving x > 5 or x < -1.

Question 3

Which value satisfies 2x + 3 > 11?

Accepted Answer

x = 5

Answer

2x + 3 > 11 gives x > 4; only x = 5 satisfies this.

Question 4

Solve: 5 - 2x < 1

Accepted Answer

x > 2

Answer

Subtract 5: -2x < -4, then divide by -2 and flip: x > 2.

Question 5

In interval notation, how is x ≥ -1 written?

Accepted Answer

[-1, ∞)

Answer

x ≥ -1 includes -1 (bracket) and extends to positive infinity: [-1, ∞).

Algebra Test Practice Test