Solving Linear Equations Flashcards

Solve for x: 4x + 9 = 29

Answer: x = 5

Subtract 9 from both sides: 4x = 20, then divide by 4: x = 5.

If a wire is cut into two pieces where one piece is twice as long as the other and the total length is 48 feet, how long is the shorter piece?

Answer: 16 feet

Let x = shorter piece; x + 2x = 48, so 3x = 48, x = 16 feet.

Solve for x: 7 - 2x = 3

Answer: x = 2

Subtract 7 from both sides: -2x = -4, then divide by -2: x = 2.

Solve for t: t/3 - 4 = 2

Answer: t = 18

Add 4 to both sides: t/3 = 6, then multiply by 3: t = 18.

An electrician charges a $75 service fee plus $45 per hour. A customer is billed $255. How many hours did the job take?

Answer: 4 hours

Set up 45h + 75 = 255, so 45h = 180, h = 4 hours.

Solve for x: 6x - 4 = 2x + 12

Answer: x = 4

Subtract 2x: 4x - 4 = 12, add 4: 4x = 16, divide: x = 4.

Solve for m: 3(m - 2) = 15

Answer: m = 7

Divide by 3: m - 2 = 5, then add 2: m = 7.