Algebraic Expressions & Equations Flashcards

If 4x − 3 = 2(x + 5), what is x?

Answer: 13/2

4x − 3 = 2x + 10 → 2x = 13 → x = 13/2.

A cab charges a $3.00 flat fee plus $1.50 per mile. If a rider paid $12.00, how many miles did they travel?

Answer: 6

3 + 1.5m = 12 → 1.5m = 9 → m = 6 miles.

Which expression represents 'five less than three times a number n'?

Answer: 3n − 5

'Three times a number' is 3n, and 'five less than' means subtract 5 from it: 3n − 5.

For what value of k does the equation 3x + k = 5x − 4 have the solution x = 7?

Answer: 10

Substituting x = 7: 21 + k = 35 − 4 = 31, so k = 10.

Which of the following is equivalent to 3x(2x − 5) + 4(2x − 5)?

Answer: (3x + 4)(2x − 5)

Both terms share the factor (2x − 5), so factoring it out gives (3x + 4)(2x − 5).

If 3 − x ≤ 7, which describes the solution set?

Answer: x ≥ −4

3 − x ≤ 7 → −x ≤ 4 → x ≥ −4 (flip the inequality when multiplying by −1).

Which of the following equations represents a line that passes through (0, −3) with slope 2?

Answer: y = 2x − 3

Slope-intercept form y = mx + b with m = 2 and b = −3 gives y = 2x − 3.