1. Section 2-3 Solve Multi-step Equations SPI 22D: Solve multi-step equations with variables on one side
Objectives:
Solve multi-step linear equations by combining like terms and using the distributive property
Recall distributive property
9(w – 6) = 9w + (-54) or 9w - 54
Recall combining like terms:
4c + 5c = (4 + 5)c = 9c
Can NOT combine 8x x2.

2. Solve a two-step Linear Equation
Step 1. Combine like terms
Step 2. Circle term with variable
Step 3. Do all addition and subtraction to get like terms on
one side
Step 4. Simplify
Step 5. Do multiplication and division
Step 6. Check your answer
Solve 3a a = 90
4a + 6 = 90 Combine like terms.
3a a = 90
Check:
3(21) Substitute 21 for a.
90 = 90
4a + 6 – 6 = 90 – 6 Subtract 6 from each side.
4a = 84 Simplify.
4a 4
84 4
= Divide each side by 4.
a = 21 Simplify.

3. Try It! Solve a two-step Linear Equation
Solve 2b 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.
3b 3
84 3
Solve a two-step Linear Equation with Grouping Symbols
Solve 2(x – 3) = 8
2x – 6 = 8 Use the Distributive Property.
2x – = Add 6 to each side.
2x = 14 Simplify.
= Divide each side by 2.
2x 2
14 2
x = 7 Simplify.

4. Real-world: Write and Solve a Two-step Linear Equation
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?
Draw and label a diagram to model the problem.
Define a variable
Write an equation
x x = 63
2x + 25 = 63 Combine like terms.
2x + 25 – 25 = 63 – 25 Subtract 25 from each side.
2x = 38 Simplify.
= Divide each side by 2.
2x 2
38 2
x = 19
The pen can be 19 ft long.

5. Solve Linear Equations with Fractions
Two Methods:
1. Find common denominator
2. Multiply to clear fractions
Method 1: Find a common denominator

6. Method 2: Multiply to Clear Fractions
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

7. Linear Equations and Fractions
Try It!
Linear Equations and Fractions
Multiply each term by 8
Simplify
Subtraction Property of Equality
Simplify
Division Property of Equality

8. 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 $ They spent a total of $ 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) = 41
5.00h – 6.00 =
5.00h = 35
h = 7

9. Summary for Solving a Multi-Step Linear Equation
Clear equations of fractions and decimals
2. Use the distributive property to remove parentheses on each side
Combine like terms
Undo addition or subtraction
5. Undo multiplication and division