Linear Equations in One Variable Flashcards

Solve for x: 8x − (2x + 4) = 20

Answer: 4

6x − 4 = 20 → 6x = 24 → x = 4.

A water tank holds 600 liters. It is being drained at 25 liters per minute. After m minutes, 250 liters remain. What is m?

Answer: 16

600 − 25m = 250 → 25m = 350 → m = 14.

For the equation 3x − 7 = bx + 5, what value of b makes x = 6 the solution?

Answer: 1

3(6) − 7 = 6b + 5 → 11 = 6b + 5 → 6b = 6 → b = 1.

Solve for x: (3x + 1)/2 = (x − 3)/4 + 5

Answer: 3

Multiply through by 4: 2(3x + 1) = (x − 3) + 20 → 6x + 2 = x + 17 → 5x = 15 → x = 3.

A shop sells two types of gift bags. Type X sells for $6 and Type Y for $9. A customer buys 8 bags and pays $57. How many Type X bags were purchased?

Answer: 5

Let x be Type X: 6x + 9(8 − x) = 57 → 6x + 72 − 9x = 57 → −3x = −15 → x = 5.

If 14 − x = 3(x − 2), what is the value of x?

Answer: 5

14 − x = 3x − 6 → 20 = 4x → x = 5.

Solve for x: 1.2x − 0.6 = 0.6x + 1.8

Answer: 4

0.6x = 2.4 → x = 4.