solving equations with steps

Solving Equations Solving Equations with Stepswith Steps

(Barb’s Nazi Way…)(Barb’s Nazi Way…)

Have a white board/marker/wipe and a calculator…

DefinitionsDefinitions

• An EQUATION is a math sentence.– It contains two expressions, separated by

the equals sign (=).

• The WALL is merely two parallel bars drawn to separate the two expressions.

• INVERSES are operations that undo each other.

• P--E--MD--AS is done backwards.

Just Checking…Just Checking…

• What is an equation?

• How is it different from an expression?

• What is the wall?

• What are inverses?

• Give 3 examples of inverses.

• How is P--E--MD--AS done?

Example: 3x + -2 = -7Example: 3x + -2 = -7

• Why is this an equation?• What are the two expressions in

this equation?• Which one of the expressions is in

simplest form?

Steps to solve equations:Steps to solve equations:1. Copy the problem.2. Draw the wall.3. Recopy the problem (leave a little space on the

left).4. Do backwards! Use inverse operations

on both sides of the equal sign.

5. Solve like expressions - answer underneath.6. Cloud answer.7. Write the check and arrow up to original

answer.

P

E

MD

AS

SolveSolve

4x + 5 = 15

SolveSolve

4x + 5 = 15

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1

1

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

1

1

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

x = 2.5

1

1

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

x = 2.5

1

1

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

x = 2.5

1

1

Check: 4 • 2.5 + 5 10 + 5 = 15

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

x = 2.5

1

1

Check: 4 • 2.5 + 5 10 + 5 = 15

SolveSolve

4x + 5 = 15

4x + 5 - 5 = 15 - 5

4x + 0 = 10

4x = 10

4 4

1x = 2.5

x = 2.5

1

1

Check: 4 • 2.5 + 5 10 + 5 = 15

Try these:Try these:

1. 125 + 3b = 154.97

2. 4t + 7 = 3

3. 15 = 3y - (-6)

4. n / (-8) + 2 = -3

5. 30 = x / 3 - 9

6. -4.2 = 23 + 8a

Bonus: 3n + 9 + 4n = 2