Math Algebra Flashcards

If 3x - 7 = 2x + 5, what is the value of x?

Answer: 12

Subtracting 2x from both sides gives x - 7 = 5, so x = 12.

Which value of x satisfies |2x - 4| = 10?

Answer: x = 7 or x = -3

Setting 2x - 4 = 10 gives x = 7, and setting 2x - 4 = -10 gives x = -3.

A line passes through (0, -3) and (4, 5). What is its equation?

Answer: y = 2x - 3

The slope is (5 - (-3))/(4 - 0) = 2 and the y-intercept is -3, giving y = 2x - 3.

If f(x) = 4x² - 9, which expression equals f(x) in factored form?

Answer: (2x - 3)(2x + 3)

4x² - 9 is a difference of squares: (2x)² - 3² = (2x - 3)(2x + 3).

What is the solution set of 5 - 2x ≥ 11?

Answer: x ≤ -3

Subtracting 5 gives -2x ≥ 6, then dividing by -2 (flip inequality) gives x ≤ -3.

If (x + 3)(x - 5) = 0, what are the solutions for x?

Answer: x = -3 and x = 5

Setting each factor equal to zero: x + 3 = 0 → x = -3 and x - 5 = 0 → x = 5.

For what value(s) of x is the expression (x² - 16)/(x - 4) undefined?

Answer: x = 4 only

The expression is undefined when the denominator equals zero: x - 4 = 0, so x = 4.