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 = -24/5 or -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

Problem Solving

100

Michael travels 315 miles in 7.1 hours. What is his average speed to the nearest hundredth?

44.37 mph

200

Terry takes 3.9 hours to study for her math test. How many minutes is she studying?

234 minutes

300

One elephant runs 10 mph for 45 minutes. How many miles does the elephant run?

7.5 miles

400

Joseph is building a rectangular garden. He has 30 feet of fencing. The width of the garden must be 8 feet. What is the length of the garden?

L = 14 ft

500

Two men are hiking an eleven mile stretch of the Ozark Highlands Trail. The first man begins his hike at 7 a.m. and travels at 4 mph. The second man begins his hike at 8 a.m. and hikes at 3 mph. If both men travel the same distance, who finishes first?

The first man! He travels for 3 hours and 40 minutes and finishes at 10:40 a.m. The second man travels for 2 hours and 45 minutes, and finishes at 10:45 a.m.

Decimal Equations

100

2.1x = 4.2

x = 2

200

3.4x - 0.4 = 2.7

x = ~0.9

300

0.56g - 3.19 = 4.51g + 0.76

g = -1

400

13.9(2.1k + 3.7) = -2.7 - 4.5k Round to the nearest tenth.

k = ~1.7

500

8.1(q - 9.33) = -2.71(-3.6 - 2q) + 2.11q Round to the nearest integer.

q = ~150