Solving Linear Equations

Two-Step Equations

100

Solve: 2x + 4 = 16

x = 6

200

Solve: 3x − 5 = 16

x = 7

300

Solve: x/4 + 3 = 8

x = 20

400

 Solve: 5x + 7 = 42

x = 7

500

Solve: −2x + 9 = 21

x = -6

Multi-Step Equations

100

Solve: 3(x + 2) = 21

x = 5

200

Solve: 2(x − 4) + 6 = 18

x = 10

300

Solve: 4[2x + 1] − 8 = 24

x = 3.5

400

Solve: 3(2x − 5) + 4 = 19

 x = 5

500

Solve: 2[3(x − 1) + 4] = 20

x = 3

Variables on Both Sides

100

2x + 3 = x + 11

x = 8

200

Solve: 5x − 4 = 2x + 11

x = 5

300

 Solve: 7x + 2 = 4x + 20

x = 6

400

9x − 5 = 3x + 19

x = 4

500

Solve: 4(x − 2) = 2x + 8

x = 8

Error Analysis

100

A student solved: x + 6 = 10 

x = 16 

What mistake was made?

The student added 6 instead of subtracting 6.

200

A student solved: 3x = 18 

x = 15 

What mistake was made?

The student divided incorrectly. 18 ÷ 3 = 6.

300

A student solved: 2(x + 4) = 10 

2x + 4 = 10 

What mistake was made?

The student did not distribute the 2 to both terms.

400

A student solved: 5x − 2 = 3x + 8 

2x − 2 = 8 

What mistake was made?

The equation setup is incomplete. The student still needs to add 2 to both sides and solve.

500

A student solved: 4x + 6 = 4x − 3 

x = −9 

What mistake was made?

The variables cancel out, leaving 6 = −3, which is false. The equation has no solution.

Real-World Algebra

100

A movie ticket costs $12. You have $48. How many tickets can you buy? 

Must show the equations AND the answer!

Equation: 12x = 48

x = 4 tickets

200

A gym charges a $10 fee plus $15 per month. Your total is $70. 

Must show the equation AND the answer!

Equation: 15x + 10 = 70

x = 4 months

300

A streaming service charges a $12 sign-up fee plus $5 per month. Another service charges $3 per month plus a $20 sign-up fee. After how many months will the costs be the same?

Must show the equation AND the answer!

Equation: 5x + 12 = 3x + 20

x = 4 months

400

A school fundraiser sells shirts online and in person. Online sales earn $8 per shirt plus a $30 bonus. In-person sales earn $10 per shirt plus a $10 bonus. How many shirts sold will make the profits equal?

Must show the equation AND the answer!

Equation: 8x + 30 = 10x + 10

x = 10 shirts

500

The same four friends buy tickets for two shows on consecutive nights. They use a coupon for $5 off each ticket. They pay a total of $416 for 8 tickets. Find the original price of the tickets. 

Must show the equation AND the answer!

Equation: 8(x - 5) = 416

x = 57