Solving MultiStep Equations

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Solving Multi-Step Equations
Created by Kenny Kong HKIS 200
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Lesson Objectives

• Know the basic rule for solving equations is
  When you do something to one side of an equation,
  you must do the same thing to the other side of
  the equation.
• know that you have solved an equation when the
  variable is alone (isolated) on one side of the
  equation and the variable is positive.

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Lesson Objectives Cont

• Know how to set up equation for word problems.
• Know that solving equations that have a fraction
  in front of the variable use the multiplicative
  inverse of the coefficient (inverting the number
  or turning it upside down.)

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Basic Rule for Solving Equation

• When you do something to one side of an equation,
  you must do the same thing to the other side of
  the equation.
• When the variable is alone (isolated) on one side
  of the equation and the variable is positive, you
  have solved an equation.

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Example 4x 1 21
4x 1 21

• Subtract 1 from both sides of the equation.

4x 1 21
? 1 ? 1

• Simplify both sides of the equation.

4x 20
4x 20

• Divide by 4 to both sides of the equation.

• Simplify both sides of the equation.

x 5
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Example 5x ? 3 37
5x ? 3 37

• Add 3 to both sides of the equation.

5x ? 3 37
3 3

• Simplify both sides of the equation.

5x 40
5x 40

• Divide by 5 to both sides of the equation.

• Simplify both sides of the equation.

x 8
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Example x/9 4 11
x/9 4 11

• Subtract 4 from both sides of the equation.

x/9 4 11
? 4 ? 4

• Simplify both sides of the equation.

x/9 7

• Multiply by 9 to both sides of the equation.

x/9 7
9 9

• Simplify both sides of the equation.

x 63
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Example 15 9? 2x
15 9? 2x

• Subtract 9 to both sides of the equation.

15 9 ? 2x
? 9 ? 9

• Simplify both sides of the equation.

6 -2x
6 -2x

• Divide by -2 to both sides of the equation.

• Simplify both sides of the equation.

-3 x
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Checking Your Answers

• Check your answer to tell if you got the correct
  answer to an equation
• When you replace the variable with your answer,
  you should get a true statement.

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Example of Check your answers

• The answer you got for this problem is -2.

26x 3 -49

• Substitute the variable x with -2.

26(-2) 3 -49
-49 -49 is a true statement.

• Simplify the left side of the equation.

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Setting Up Equations for Word Problems

• You received a raise in your hourly rate of pay.
• Your new rate of pay is 11 an hour.
• You are now earning 5 more than 3/5 your
  original wage.
• How much did you make before you got your raise?
  What was your raise?
• Let x the original rate of pay in per hour.
• Then 5 3/5x 11

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Solution
5 3/5x 11

• Subtract 5 from both sides of the equation.

5 3/5x 11
? 5 ? 5

• Simplify both sides of the equation.

3/5x 6

• Multiply by 5/3 to both sides of the equation.

3/5 x 6
5/3 5/3

• Simplify both sides of the equation.

x 10
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Setting Up Equations for Word Problems

• You work at a gift shop and have a 20 employee
  discount on any regularly priced merchandise you
  buy.
• You found a sale-priced item of 24.
• You have 100 to spend for gifts.
• How much can you spend on regularly priced items?
• Let x regular priced merchandise.
• If you received a discount of 20, then you are
  paying 80 (or 0.8) of the regular price.

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Solution
24 0.8x 100

• Subtract 24 from both sides of the equation.

24 0.8x 100
? 24 ? 24

• Simplify both sides of the equation.

0.8x 76

• Multiply by 0.8 to both sides of the equation.

0.8x 76

• Simplify both sides of the equation.

x 95
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Solving Equations that have a Fraction in front
of the Variable

• To solve an equation with a fraction for a
  coefficient, we multiply by the multiplicative
  inverse of the coefficient.
• Multiplicative inverse of a number is inverting
  the number or turning it upside down.
• A number times its multiplicative inverse will
  always equal 1.

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Example 4/3 x 5 17
4/3 x 5 17

• Subtract 5 from both sides of the equation.

4/3 x 5 17
? 5 ? 5

• Simplify both sides of the equation.

4/3x 12

• Multiply by the multiplicative inverse of 3/4 to
  both sides of the equation.

4/3 x 12
3/4 3/4

• Simplify both sides of the equation.

x 9
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Example 2/3 x ? 4 -22
2/3 x ? 4 -22

• Add 4 to both sides of the equation.

2/3 x ? 4 -22
4 4

• Simplify both sides of the equation.

2/3x -18

• Multiply by the multiplicative inverse of 3/2 to
  both sides of the equation.

2/3 x -18
3/2 3/2

• Simplify both sides of the equation.

x -27