Objectives: •Solve multi-step linear equations by combining like terms and using the distributive property

Recall combining like terms: • 4c + 5c = (4 + 5)c = 9c • Can NOT combine 8x + 15 + x2.

Recall distributive property

• 9(w – 6) = 9w + (-54) or 9w - 54

Section 2-3 Solve Multi-step Equations

SPI 22D: Solve multi-step equations with variables on one side

Solve 3a + 6 + a = 90

4a + 6 = 90 Combine like terms.4a + 6 – 6 = 90 – 6 Subtract 6 from each side.

4a = 84 Simplify.

= Divide each side by 4.

a = 21 Simplify.

4a4

844

Solve a two-step Linear Equation

Step 1. Combine like termsStep 2. Circle term with variableStep 3. Do all addition and subtraction to get like terms on one sideStep 4. SimplifyStep 5. Do multiplication and divisionStep 6. Check your answer

3a + 6 + a = 90Check:

3(21) + 6 + 21 90 Substitute 21 for a.

63 + 6 + 21 90

90 = 90

Solve 2(x – 3) = 8

2x – 6 = 8 Use the Distributive Property.

2x – 6 + 6 = 8 + 6 Add 6 to each side.

2x = 14 Simplify.

x = 7 Simplify.

= Divide each side by 2. 2x2

142

Solve a two-step Linear Equation

Solve 2b + 6 + b = 90

3b + 6 = 90 Combine like terms.

3b + 6 – 6 = 90 – 6 Subtract 6 from each side.

3b = 84 Simplify.

= Divide each side by 4.

b = 28 Simplify.

3b3

843

Solve a two-step Linear Equation with Grouping Symbols

You need to build a rectangular pen in your back yard for your dog.

One side of the pen will be against the house. Two sides of the pen

have a length of x ft and the width will be 25 ft. What is the greatest

length the pen can be if you have 63 ft of fencing?

x + 25 + x = 63

The pen can be 19 ft long.

2x + 25 = 63 Combine like terms.

2x + 25 – 25 = 63 – 25 Subtract 25 from each side.

2x = 38 Simplify.

x = 19

= Divide each side by 2. 2x2

382

Real-world: Write and Solve a Two-step Linear Equation

Draw and label a diagram to model the problem.Define a variableWrite an equation

Two Methods: 1. Find common denominator2. Multiply to clear fractions

Solve Linear Equations with Fractions

1752

3xx

rdenominatocommon using Rewrite 1710

2

10

15 xx

Method 1: Find a common denominator

termslike Combine 1710

17x

lrecriproca by the sideeach Multiply 17

1017

10

17

17

10 x

Simplify 10x

Method 2: Multiply to Clear Fractions

1752

3xx

17)10(52

310

xx

17)10(5

102

310

xx

1705

10

2

30 xx

170215 xx

17017 x

10x

Multiply each term by 10 (common multiple of 2 and 5)

Rewrite equation using distributive property

Simplify

Simplify

Combine like terms

Division Property of Equality

Linear Equations and Fractions

5.12

11

2

3

8

12x

128 x

57558 x

758 x

8

78

8

58

18x

8

7

8

5x

Multiply each term by 8

Simplify

Subtraction Property of Equality

Simplify

Division Property of Equality

Real-World: The Canoe Trip

John and two friends went on a canoe trip. The cost of renting the canoe is $5.00 per hour. In addition, each person must rent a life jacket which costs $2.00. They spent a total of $41.00. For how many hours did they rent the canoe?

1. Define the variable h=numbers of hours for canoe

2. Write an equation relating total cost, # hours and cost of life vests.

5.00h + 3(2.00) = 41

3. Solve the equation for h.

5.00h + 3(2.00) = 415.00h + 6.00 – 6.00 = 41 -6.00 5.00h = 35 h = 7

Summary for Solving a Multi-Step Linear Equation

1. Clear equations of fractions and decimals

2. Use the distributive property to remove parentheses on each side

3. Combine like terms

4. Undo addition or subtraction

5. Undo multiplication and division