Linear Equations in One Variable Flashcards

If 2(x + 5) = 3(x − 2), what is the value of x?

Answer: x = 16

Expand: 2x + 10 = 3x − 6; subtract 2x: 10 = x − 6; x = 16.

A taxi charges $2.50 plus $1.80 per mile. The total fare was $11.50. How many miles did the passenger travel?

Answer: 5 miles

2.50 + 1.80m = 11.50 → 1.80m = 9 → m = 5.

For the equation ax + 6 = 18 to have the solution x = 4, what must a equal?

Answer: a = 3

4a + 6 = 18 → 4a = 12 → a = 3.

Solve for x: (2x − 3)/5 = 3

Answer: x = 9

Multiply both sides by 5: 2x − 3 = 15; add 3: 2x = 18; x = 9.

Marcus earns $15 per hour and has already earned $120 this week. How many more hours must he work to earn at least $195 total?

Answer: 5 hours

Additional needed: (195 − 120)/15 = 75/15 = 5 hours.

Solve for x: 6 − (3 − x) = 2x − 1

Answer: x = 4

Simplify left side: 3 + x = 2x − 1 → 4 = x.

In the equation 5x − c = 2x + 9, if x = 4, what is the value of c?

Answer: c = 3

20 − c = 8 + 9 = 17 → c = 3.