Digital SAT Math Algebra Practice Flashcards

What is the solution set for the equation |2x − 5| = 9?

Answer: x = 7 or x = −2

Set up two cases: 2x − 5 = 9 → x = 7, and 2x − 5 = −9 → x = −2.

A gym charges a $40 registration fee plus $25 per month. A competing gym charges no registration fee but $35 per month. After how many months will the total cost at both gyms be equal?

Answer: 4

Set 40 + 25m = 35m → 40 = 10m → m = 4 months.

If the function h is defined by h(x) = ax + b, and h(1) = 5 and h(3) = 11, what is the value of a + b?

Answer: 5

From h(1)=5: a+b=5. From h(3)=11: 3a+b=11. Subtracting: 2a=6, a=3, b=2. So a+b=5.

Which equation represents a line parallel to y = −(1/2)x + 7 that passes through (4, 1)?

Answer: y = −(1/2)x + 3

Parallel lines share the same slope −1/2. Use point-slope: y − 1 = −(1/2)(x − 4) → y = −(1/2)x + 3.

The total number of items n in a shipment is modeled by n = 15b + 8, where b is the number of boxes. If n = 83, how many boxes are in the shipment?

Answer: 5

83 = 15b + 8 → 15b = 75 → b = 5.

If f(x) = x² − 6x + 8, which of the following is an equivalent factored form?

Answer: (x − 2)(x − 4)

Find two numbers that multiply to 8 and add to −6: −2 and −4. So (x − 2)(x − 4).

A car travels at an average speed of v miles per hour for t hours. If the car covers 210 miles and v = 3t + 15, which equation can be used to find t?

Answer: 3t² + 15t = 210

Distance = speed × time → 210 = v × t = (3t + 15)t = 3t² + 15t.