Linear Inequalities in One or Two Variables Flashcards

Solve for x: 4x − (2x + 3) > 9

Answer: x > 6

4x − 2x − 3 > 9 → 2x > 12 → x > 6.

A fruit stand sells apples for $0.60 each and pears for $0.90 each. Mia spends less than $9.00. If she buys 6 apples, what is the maximum number of whole pears p she can buy?

Answer: 5

0.60(6) + 0.90p < 9.00 → 3.60 + 0.90p < 9.00 → 0.90p < 5.40 → p < 6; the largest whole number strictly less than 6 is 5.

The inequality 5 − x/3 < 3 is equivalent to which of the following?

Answer: x > 6

−x/3 2 → x > 6.

If 0 < 3x + 6 < 18, what is the range of x?

Answer: −2 < x < 4

Subtract 6 from all parts: −6 < 3x < 12 → −2 < x < 4.

Which of the following inequalities has no solution?

Answer: x > 5 and x < 2

x > 5 and x < 2 requires x to be simultaneously greater than 5 and less than 2, which is impossible.

A recipe requires flour and sugar with a combined weight of at most 5 cups. If flour f is at least 2 cups, which system represents these constraints?

Answer: f ≥ 2 and f + s ≤ 5

'At least 2' means f ≥ 2; 'at most 5' means f + s ≤ 5.

Solve for x: 3(2x − 1) ≥ 2(3x + 4)

Answer: No solution

6x − 3 ≥ 6x + 8 → −3 ≥ 8, which is false for all x; the inequality has no solution.

Elena needs to buy at least 40 stamps total. Forever stamps cost $0.68 and postcard stamps cost $0.53. She has $26. Which constraint ensures she has enough money?

Answer: 0.68f + 0.53p ≤ 26

The money spent on stamps must not exceed her $26 budget, so 0.68f + 0.53p ≤ 26.