All the Steps!

All the Steps!

By Jai Johnson

What we do to one side of the equation we must do to the other.

Keep it equal!

Remove numbers on the same side of the equation as x by using inverse (or opposite) operations

Get "x" by itself

Two Rules of Solving Equations

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GET READY!

What inverse operation should you do to solve for x on the following problems?

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Multiple Choice

x - 4 = 10

• add 4

• subtract 4

• multiply by 4

• divide by 4

Multiple Choice

$$\frac{x}{6}=3$$  

• add 6

• subtract 6

• multiply by 6

• divide by 6

Multiple Choice

-2 = x + 9

• add 9

• subtract 9

• multiply by 9

• divide by 9

Multiple Choice

-2 = 9 + x

• add 9

• subtract 9

• multiply by 9

• divide by 9

Multiple Choice

-2 = -9 + x

• add 9

• subtract 9

• multiply by -9

• subtract x

Multiple Choice

8x = 16

• add 8

• subtract 8

• multiply by 8

• divide by 8

Multiple Choice

$$15=\frac{3}{4}x$$  

• add 3/4

• subtract 3/4

• multiply by 3/4

• divide by 3/4

Multiple Choice

93.4781 + x = 18924.92

• add 93.4781

• subtract 93.4781

• multiply by 93.4781

• divide by 93.4781

Remove any numbers that are being multiplied or divided by x

2) Multiply or divide

Remove any numbers that are being added to or subtracted from x

1) Add or subtract

Two-Step Equations

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GET READY

What is the FIRST step to solving the following problems?

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Multiple Choice

5x - 2 = 13

• Add 2

• Subtract 13

• Multiply by 5

• Divide by 5

Multiple Choice

$$\frac{2}{3}x+4\ =\ 18$$  

• Add 4

• Subtract 4

• Multiply by 2/3

• Divide by 2/3

Multiple Choice

58 = 9 + 7x

• Add 9

• Subtract 9

• Add 58

• Subtract 58

Multiple Choice

$$-6\ +\ \frac{1}{8}x\ =\ 1$$  

• Add 6

• Subtract 6

• Add 1/8

• Subtract 1/8

WAIT! AN EXCEPTION!

If EVERYTHING is being multiplied or divided by a value, remove that value FIRST!

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Multiple Choice

12(x - 4) = 36

• Add 4

• Subtract 4

• Multiply by 12

• Divide by 12

Multiple Choice

42 = -6(x - 3)

• Add 6

• Subtract 6

• Multiply by -6

• Divide by -6

Multiple Choice

$$\frac{3+x}{5}=-4$$  

• Add 3

• Subtract 3

• Multiply by 5

• Divide by 5

TIME TO SOLVE!

Grab your white boards and calculators!

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Multiple Choice

x - 4 = 10

• 14

• 6

• -40

• -2.5

Multiple Choice

$$\frac{x}{6}=3$$

• 9

• -3

• 18

• 0.5

Multiple Choice

-2 = x + 9

• 7

• -11

• -7

• 11

Multiple Choice

8x = 16

• 24

• 8

• 128

• 2

HOW TO DIVIDE BY A FRACTION

Multiply by its "reciprocal" (or its re-flip-rocal)

Flip it and multiply:

​

Instead of dividing by 2/3, multiply by 3/2. 2/3x = 14

​

Instead of dividing by 1/5, multiply by 5/1.​ 1/5x = -3

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Multiple Choice

$$15=\frac{3}{4}x$$  

• 11.25

• 20

• 5

• 60

Multiple Choice

5x - 2 = 13

• 3

• 2.2

• 75

• 10

Multiple Choice

2x + 1 = 9

• 5

• 4

• 20

• 16

Multiple Choice

$$\frac{2}{3}x+4=18$$  

• 9.33

• 21

• 8

• 23

Multiple Choice

58 = 9 + 7x

• 42

• 60

• 7

• 343

Multiple Choice

12(x - 4) = 36

• 3.33

• 2.66

• -1

• 7

Multiple Choice

42 = -6(x - 3)

• 4

• 10

• -4

• -10

Multistep Problems

1) Distribute parentheses

2) Get your x's in Texas

3) Solve for x​

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GET READY!

What is the first step to solving these problems?

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Multiple Choice

5x + 1 = 4(3x - 5)

• Subtract 1

• Subtract 5x

• Distribute the 4

• Add 5

Multiple Choice

NOW SOLVE!

5x + 1 = 4(3x - 5)

• 3

• 6/7

• -3

• -1

Multiple Choice

24 = 3x - 6 + 7x

• Subtract 24

• Subtract 3x

• Add 6

• Add the x's

Multiple Choice

NOW SOLVE!

24 = 3x - 6 + 7x

• -3

• 3

• no solution

• infinite solutions

Multiple Choice

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

• Divide by -2

• Distribute -2

• Subtract 5

• Add 2x

Multiple Choice

NOW SOLVE!

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

• -2

• 7

• no solution

• infinite solutions

Multiple Choice

10 + 4x = 2(2x + 5)

• Subtract 10

• Subtract 4x

• Distribute 2

• Divide by 2

Multiple Choice

NOW SOLVE!

10 + 4x = 2(2x + 5)

• 0

• 5

• no solution

• infinite solutions