Solving One-Variable Equations

One-Step Equations

100

x = 3 - 9

x = -6

200

3 + g = -17

g = -20

300

-19 + w = 13

w = 32

400

7x = 126

x = 18

500

p/3 = -9

p = -27

Multi-step Equations

100

2p + 1 = 21

p = 10

200

7p - 9 = -30

p = -3

300

2(x + 1) = 18

x = 8

400

6(t - 3) = -60

t = -7

500

5y + 5(y - 3) = -63

y = -4.8

Variables on Both Sides

100

2x = x + 5

x = 5

200

x + 1 = 3x - 5

x = 3

300

2(3c - 8) = -8c - 2

c = 1

400

-2(-7a + 4) = 5(a - 16)

a = -8

500

-3(d - 1) = d/5 + 3

d = 0

All Types of Equations

100

3x=129

x = 43

200

(x-6) / 3=14

x = 48

300

8+(x/4)=11

12

400

4x / 5 = 3 / 15

x = .25

500

2x-10+5=4x-9

x = 2

Word Problems

100

Six pine trees were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at a constant rate per year. Let h be the height of the trees after y years. What is the growth rate of the trees?

h=0.75y+2 

0.75 units per year

200

Sarah owns a shipping company. She charges a flat fee of $20 plus $5 per kilometer for deliveries. She wants to make $150 on a delivery. Let d be the distance of the delivery. Write an equation to represent this situation.

5d+20=150

300

Hartz Rental Car Company charges $19.95 per day plus $0.10 per mile to rent a compact car. Lee rented a car for two days and the total bill was $89.75. Write an equation where x is the number of miles driven. 

39.90+0.10x=89.75

400

Paul wants to fence in his garden to prevent this dog from digging it up. He will use 66 meters of fencing. Paul wants the length of the garden to be twice the width. Write an equation to represent the situation where x is the width.

x+x+2x+2x=66

(or 6x=66)

500

The Jones family is taking a trip from Seattle, WA to San Diego, CA over the course of 3 days. They plan on traveling 200 miles more on the second day than they will on the first day. They will travel 75 miles less on the third day than they will on the first day. To total distance of the trip is 1058 miles. Write an equation to represent the situation where x is the number of miles traveled on the first day.

x+x+200+x-75=1058

(or 3x+125=1058)