Linear Equations in One Variable Flashcards

Solve for x: (5x − 3)/4 = (3x + 1)/2

Answer: −5

5x − 3 = 2(3x + 1) → 5x − 3 = 6x + 2 → −x = 5 → x = −5.

A charity sells raffle tickets at $4 each and event tickets at $7 each. In total, 50 tickets are sold for $260. How many raffle tickets were sold?

Answer: 30

4r + 7(50 − r) = 260 → 4r + 350 − 7r = 260 → −3r = −90 → r = 30.

If 7 − 2(3x − 1) = 3, what is x?

Answer: 1

7 − 6x + 2 = 3 → 9 − 6x = 3 → 6x = 6 → x = 1.

A fitness tracker shows that Emily burns 8 calories per minute of running. After a workout she had burned 360 calories total, including 40 calories from warm-up. How many minutes did she run?

Answer: 45

8m + 40 = 360 → 8m = 320 → m = 40.

In the equation 4x + r = 2x − 5, if r = 3 what is x?

Answer: −4

4x + 3 = 2x − 5 → 2x = −8 → x = −4.

Solve for x: 4(x − 2) = 2(x + 1) + 2

Answer: 6

4x − 8 = 2x + 2 + 2 → 4x − 8 = 2x + 4 → 2x = 12 → x = 6.

A ladder is 3 feet shorter than twice the height of a wall. The ladder is 15 feet long. How tall is the wall?

Answer: 9

2h − 3 = 15 → 2h = 18 → h = 9.