Math Algebra Flashcards

If f(x) = 3x - 2 and g(x) = x + 4, for what value of x does f(x) = g(x)?

Answer: x = 3

Setting 3x - 2 = x + 4 gives 2x = 6, so x = 3.

A line has equation 4x - 2y = 10. What is the slope of this line?

Answer: 2

Rewriting in slope-intercept form: y = 2x - 5, so the slope is 2.

What is the solution to the system: y = x + 1 and y = -x + 7?

Answer: (3, 4)

Setting x + 1 = -x + 7 gives 2x = 6, so x = 3 and y = 4.

Which expression represents the product (2x - 3)(x + 5)?

Answer: 2x² + 7x - 15

Using FOIL: 2x·x + 2x·5 + (-3)·x + (-3)·5 = 2x² + 10x - 3x - 15 = 2x² + 7x - 15.

Jayla saves $120 initially and adds $15 per week. Marcus has $30 and saves $25 per week. After how many weeks will they have the same amount?

Answer: 9

Setting 120 + 15w = 30 + 25w gives 90 = 10w, so w = 9 weeks.

If x² = 81, which of the following gives all possible values of x?

Answer: x = 9 or x = -9

Taking the square root of both sides gives x = ±9, since both (9)² and (-9)² equal 81.

The expression 6x² + 11x - 10 factors as (2x + 5)(3x - 2). What are the zeros of f(x) = 6x² + 11x - 10?

Answer: x = -5/2 and x = 2/3

Setting each factor to zero: 2x + 5 = 0 → x = -5/2 and 3x - 2 = 0 → x = 2/3.