Solving Multi-Step Equations

Solving Linear Equations (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 Linear Equations(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

Simplifying Expressions

100

8b + 3b

11b

200

19x - 24x

-5x

300

3 + 5(a + 4)

5a + 23

400

- (2b - 4)

-2b + 4

500

7(t + 8.5) - 5t + 4

2t + 63.5

Solving Quadratic Equations

100

x² - 7x + 12 =0

{3, 4}

200

x² - 121 = 0

{-11, 11}

300

2x² - 7x - 15 = 0

{-3/2, 5}

400

36x² + 48x = -16

{-2/3}

500

A juggler tosses a ball into the air. The ball leaves the juggler's hand 4 feet above the ground and has an initial vertical velocity of 40 feet per second. The juggler catches the ball when it falls back to a height of 3 feet. How long is the ball in the air, to the nearest tenth? The equation can be modeled as the following: -16t² + 40t + 4= 3

Approximately 2.5 seconds

Solving Mixed Equations(Variables on Both Sides)

100

7x + 1 = 2x - 9

x = -2

200

6x + 2 = -2x + 3 + 8x

no solution

300

4(y + 1) = 5 + 4y - 1

all real numbers

400

5z² + 2z = 4z²  + 3 

{-3, 1}

500

3/5(5m + 10) = 2m - 8 - m

m = -7