Pre-Algebra Practice Test: Inequalities

0 is to the right of −3 on the number line, so 0 > −3. The number −3 itself is not included because the sign is strict.

Add 4 to both sides: x < 13. Adding does not change the direction of the sign, and the sign stays strict.

Divide by −3 and reverse the sign: x ≤ −4. Forgetting to reverse gives x ≥ −4.

Subtract 5: 2x > 6. Divide by 2: x > 3. Dividing by a positive number keeps the sign.

"At least 48" means 48 or more, so h ≥ 48. A rider who is exactly 48 inches tall may ride, which h > 48 would leave out.

The filled circle means 2 is included, and the arrow points left toward smaller numbers, so x ≤ 2. An open circle would mean x < 2.

Subtract 6: −x ≤ 4. Multiply by −1 and reverse the sign: x ≥ −4.

Solve 4n ≤ 30: n ≤ 7.5. He can only buy whole notebooks, so the greatest number is 7. Eight notebooks would cost $32.

Add 2 and divide by 5: x ≥ 3. The value 2 is less than 3, so it is not a solution. The value 3 works because the sign includes equality.

Subtract 1: x/4 < 2. Multiply by 4: x < 8. The answer 16 forgets to subtract 1 first.