Warm up

2 2

2 2

2

x 4 4 0 2. 5 4 1 0

3. 3 7 6 0

Solve for x.

4. 9x 25

5. 36 60 25 0

1. x x x

x x

x x

Review of Solving Equations

Absolute value equations

1. Isolate the absolute value

2. Set up 2 equations

3. Solve both equations

4. Remember that absolute value equations cannot be set equal to a negative value for example 25 a

1 4 12x

1 4 12x 4 4

1 16x 1 16 and 1 16x x 1 16 and 1 16x x 1 1 1 1

15 and 17x x

Multi Step Equations Variables on both sides of the equation

Steps:1st – distribute2nd – combine like terms3rd – get variables on 1 side and numbers on the other side by adding or subtracting4th – multiply or divide5th – check your answer

3b + 0 = -7b

-3b -3b

0 = -10b -10 -10

0 = b

-3 + 3b – 4 + 7 = -5b – 2b

• Step 1: Distribute• Step 2: Combine Like

Terms• Step 3: Move Variable

to 1 Side• Step 4: Undo + or – • Step 5: Undo × or ÷

6 15 1 9x x 6 16 9x x

5 16 9x 5 25x

5x

Steps for Solving Equations with Parentheses

3(2x + 5) + 1 = x - 9

To solve a proportion:• Follow these easy

Steps:

• Cross multiply

• Solve the one-step equation for the variable.

3(21) = 4(x)

63 = 4x 63 = 4X 4 4 X = 63/4

214

3 x

To solve radical equations

• Isolate the radical (if you have two radicals put one on each side of the equation

• Square both sides

• Solve for the variable

8 2 6 8 x

8 2 2 x

8 2 4 x2 4x x 2

( )8 2 22 2 x

Let’s TRY one more…

3 5x x

2 2

3 5x x

3 3 5 5x x x x

3 5x x 2 3 5x

2 8x

4x

Rational Equations

Use the LCM to multiple every term in the equation.

1 1 1

5 5

n

n n n

1 1 15

5 5

nnn n n

5 1 ( 1)n

5 1 1n

5 2 n 3 n3 n