Linear Inequalities in One or Two Variables Flashcards

If 4 − x > 1, which of the following is a possible value of x?

Answer: x = 2

−x > −3 → x < 3; only x = 2 satisfies x < 3.

Solve: 3 ≤ 5 − x < 8

Answer: −3 < x ≤ 2

Subtract 5: −2 ≤ −x < 3; multiply by −1 (flip both): −3 < x ≤ 2.

A runner burns 10 calories per minute and wants to burn more than 350 calories. Which inequality shows the minimum time t needed?

Answer: 10t > 350

'More than 350' is a strict inequality: 10t > 350.

For which integer values of x is both 2x > −6 and 3x ≤ 9 satisfied?

Answer: x = −2, −1, 0, 1, 2, 3

x > −3 and x ≤ 3; integers: −2, −1, 0, 1, 2, 3.

Which system of inequalities is satisfied by the point (2, 5)?

Answer: y ≤ 3x and y ≥ x + 2

Test (2, 5) in C: 5 ≤ 6 ✓; 5 ≥ 4 ✓.

The difference of two numbers is at least 7. The smaller number is 3. What is the minimum value of the larger number?

Answer: 10

L − 3 ≥ 7 → L ≥ 10; minimum is 10.

For what values of x is 3x − 2 strictly between 4 and 16?

Answer: 2 < x < 6

4 < 3x − 2 < 16 → 6 < 3x < 18 → 2 < x < 6.