Solving Multi-Step Equations

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

3a + 12 - 6a = -9

a = 7

400

-6 = -3y + 4 + 5y

y = -5

500

78 = 3c + 12 - c + 4

c = 31

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

-2(x - 9) = -24

x = 21

500

-13(4 + 2a) = 208

a = -10

Miscellaneous

100

Which property of real numbers is shown below?

(12 • 6) • 2 = 12 • (6 • 2)

Associative Property of Multiplication

200

Evaluate the expression given a=4 and b=–3

–b² – b(a – b²)

–24

300

Does the equation y² = x represent a function?

No!

400

The median income for US females with a doctorate degree rose from $40,172 in 1990 to $60,733 in 2000. The median income for US males with a doctorate degree rose from $54,626 in 1990 to $78,092 in 2000. Which group had the greater percent increase? How much greater? (Round to the nearest percent)

US females saw a 51% increase.

US males saw a 43% increase.

US females saw a greater percent increase, by about 8%.

500

Simplify.(#8 pg 16)

4y⁹

x⁶

Equation Grab Bag

100

4x + 9 = 33

x = 6

200

x + 3x = -8

x = -2

300

4(y - 2) = -13 – y

y = -1

400

-6(m + 1) + 18 = 24

m = -2

500

7k - 8 = 52 – 2(k + 12)

k = 4

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

The Ironman Triathlon is held every year in Hawaii. The race covers a total distance of 140.6 miles. If the swim is 2.4 miles long and the bike route is 112 miles long, how long is the run?

d - run distance (in miles) 2.4+112+d=140.6 

d = 26.2 The run is 26.2 miles long. 

300

Aaron is traveling 955 miles from Phoenix, AZ to Jackson, WY. He leaves Phoenix, driving 410 miles before stopping for gas in Cortez, CO. He makes one last stop in Rock Springs, WY before traveling the final 180 miles to Jackson. Write and solve an equation to find the number of miles between Cortez and Rock Springs.

d - distance between Cortez and Rock Springs (in miles)

410+d+180 = 955 

d = 365 Aaron traveled 365 miles between Cortez and Rock Springs.

400

Sandra's brother is 6 years older than her, her sister is 2 years younger than her, and her mother is 3 times her age. Her brother, sister, and mother's combined age is 64. Write and solve an equation to find Sandra's age.

s - Sandra's age (in years)

(s+6)+(s–2)+(3s)=64 

s=12 Sandra is 12 years old.

500

Janice wants to find the value of y for the triangle shown. The perimeter of the triangle is 8y. Write and solve an equation to find the value of y.

9+8+(3y–2)=8y

y=3