Solving Equations

One-Step Equations

100

-4 = -8 + x

x= 4

200

x + 12 = -19

x= -31

300

3 = -2 + x

x= 5

400

10x = -80

x= -8

500

-16 = x+2

x= -18

Two-Step Equations

100

6x – 13 = 11

x= 4

200

3x + 5 = 14

x= 3

300

2x -6=16

x= 11

400

x/2-50=10

x= 120

500

x/3+16=89

x= 219

Distributive Property Equations

100

Solving Equations

2(x + 2) = 6

x = 1

200

Solving Equations

5(p + 2) = 20

p = 2

300

Solving Equations

2(n+5) = 4

n = -3

400

Solving Equations

5( m + 4)= -25

m = -9

500

Solving Equations

3(𝑥 − 9) = −3

x = 8

Combining Like Terms

100

Solving Equations

x + 5 - 4 = 6

x = 5

200

Solving Equations

3x + 5x = 32

x = 4

300

Solving Equations

-30 + 7 = 4x + 5

x = -7

400

Solving Equations

14=2(3a+4)

a=1

500

Solving Equations

-7 = 7(2k + 5) 

k = -3

variables both sides multi step

100

9 - 5x = 1 - x

x=2

200

-4(6x - 2) = -40 - 8x

x=3

300

-2(x + 1) = 2(x - 1)

x=0

400

-3(x + 3) = -6 (x - 3)

x=9

500

 7(x − 4) −3x + 2 = 3x − 2− x

x=12

Word problems

100

A gym charges a $20 sign-up fee and $15 per month. If you paid $80 total, how many months have you been a member?

20 + 15m = 80 

m = 4

4 months

200

A taxi company charges $3 to start the ride and $2.50 per mile. If the total cost is $18.50, how many miles did you travel?

3 + 2.5m = 18.5 

m = 6.2

6.2 miles

300

You bought 3 T-shirts and a hat for $45. If the hat costs $15, how much does each T-shirt cost?

3t + 15 = 45 

t = 10

$10

400

A babysitter charges $10 per hour plus a $5 transportation fee. If a family paid $45, how many hours did the babysitter work?

10h + 5 = 45 

h = 4

4Hours

500

At a fundraiser, tickets cost $6 each, plus a one-time table fee of $12. If the total money collected was $60, how many tickets were sold?

6t + 12 = 60 

t = 8

8 tickets

Equation Detective

100

True or False: 3x + 2 = 11 → x = 4

False

200

Identify the error: 4x + 6 = 18 → x = 6

Added 6 instead of Subtracting 6

x = 3

300

Check the solution: 5x – 3 = 17, x = 4

5 (4) - 3 = 17

20 - 3 = 17

400

The equation 2x + 5 = 13 was solved as x = 8. What’s the correct value of x?

x = 4

500

An equation reads: 3(x + 4) = 18. Student says x = 9. Correct or incorrect?

Incorrect

x = 2

Translate it

100

Translate: “8 more than a number.”

x + 8

200

Translate: “The product of a number and 5.”

5x

300

Translate: “12 less than twice a number.”

2x-12

400

Write an equation: “A number divided by 3 is equal to 7.”

x ÷ 3 = 7

or

x/3 = 7

500

Write an equation: “Four more than triple a number equals 19.”

3x + 4 = 19