Algebraic Equations and Inequalities Flashcards

Solve for x: x² = 49

Answer: x = 7 or x = -7

Taking the square root of both sides gives x = ±7, since both 7² and (-7)² equal 49.

A store sells pens for $2 each. Maria spends no more than $14. What is the maximum number of pens she can buy?

Answer: 7

The inequality 2p ≤ 14 gives p ≤ 7, so she can buy at most 7 pens.

Solve for b: b/4 - 2 = 3

Answer: b = 20

Add 2 to both sides to get b/4 = 5, then multiply by 4 to get b = 20.

Which equation has no solution?

Answer: 2x = 2x + 1

2x = 2x + 1 simplifies to 0 = 1, which is a contradiction with no solution.

Solve: -2(x - 4) = 10

Answer: x = -1

Distribute to get -2x + 8 = 10, subtract 8 to get -2x = 2, then divide by -2 to get x = -1.

The sum of three consecutive integers is 48. What is the smallest integer?

Answer: 15

Let the integers be n, n+1, n+2; then 3n + 3 = 48 gives 3n = 45, so n = 15.

Which value satisfies both x > -3 and x ≤ 1?

Answer: x = 0

x = 0 satisfies 0 > -3 (true) and 0 ≤ 1 (true); the other values fail at least one condition.