Equations

Parts of an equation

1

Define an independent variable

The part of the equation that does NOT depend on another for its value 

2

Define a dependent variable

The variable that DEPENDS on another

3

What is the independent variable in the equation: 

m = 3n² - 5n + 3

n is independent

4

What is the dependent variable in the equation:

8d - 3(d + 2) = f

f is the dependent variable

5

What is the dependent variable in the equation: 

18y + 3(y + 5) - 2y = g

g is the dependent variable

Solve One-Step Equations

1

4 = -8 + x

x= 12

2

x + 12 = 0

x= -12

3

3 = -2 – x

x= -5

4

5x = -80

x= -16

5

-16 = x+2

x= -18

Solve Two-Step Equations

1

6x – 13 = 11

x= 4

2

3x + 5 = 14

x= 3

3

(x/2) + 3 =-8

x= -22

4

(x/2) + 4 =10

x= 12

5

(x/3)=-3

x= -9

Solve Multi-Step Equations

1

4x + 3 = 7

x = 1

2

-5p + 1 = 6

p = -1

3

3(𝑥 − 9) = −3

x = 8

4

14 = (3a + 6) + 2

a=2

5

-21 = 7(5k - 8)

k = 1

Complete the Square to Solve Quadratics

1

p² + 14p - 51 = 0

{3, -17}

2

x² - 12x + 11 = 0

{11,1}

3

k² - 12k + 23 = 0

{6+ √13, 6 - √13}

4

r² - 4r - 91 = 7

{2 + √102, 2 - √102}

5

x² - 10x + 26 = 8

{5 + √7, 5 - √7}