Download Solve multi-step linear equations by combining like terms and using

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 + 15 + x2.
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 + 6 + a = 90
4aCheck:
+ 6 =3a90
+6+a
4a + 6 – 3(21)
6 = 90
– 21
6
+6+
4a 63
= 84
+ 6 + 21
4a 84 90
4 =4
a = 21
90
Combine like terms.
SubtractSubstitute
6 from each
side.
21 for a.
90
Simplify.
= 90
= 90
Divide each side by 4.
Simplify.
Solve a two-step Linear Equation
Solve 2b + 6 + b = 90
3b + 6 = 90
3b + 6 – 6 = 90 – 6
Combine like terms.
Subtract 6 from each side.
3b = 84
Simplify.
3b
84
=
3
3
Divide each side by 4.
b = 28
Simplify.
Solve a two-step Linear Equation with Grouping Symbols
Solve 2(x – 3) = 8
2x – 6 = 8
2x – 6 + 6 = 8 + 6
Use the Distributive Property.
Add 6 to each side.
2x = 14
Simplify.
2x
14
=
2
2
Divide each side by 2.
x = 7
Simplify.
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 + 25 + x = 63
2x + 25 = 63
2x + 25 – 25 = 63 – 25
Combine like terms.
Subtract 25 from each side.
2x = 38
Simplify.
2x
38
=
2
2
Divide each side by 2.
x = 19
The pen can be 19 ft long.
Solve Linear Equations with Fractions
Two Methods:
1. Find common denominator
2. Multiply to clear fractions
Method 1: Find a common denominator
3x x
  17
2 5
15
2
x  x  17
10
10
17
x  17
10
10 17
10
 x  17 
17 10
17
x  10
Rewrite using common denominato r
Combine like terms
Multiply each side by the recriproca l
Simplify
Method 2: Multiply to Clear Fractions
3x x
  17
2 5
 3x x 
10    (10)17
 2 5
Multiply each term by 10 (common multiple of 2 and 5)
 3x 
 x
10   10   (10)17
 2
5
Rewrite equation using distributive property
30
10
x  x  170
2
5
Simplify
15x  2x  170
Simplify
17 x  170
Combine like terms
x  10
Division Property of Equality
Linear Equations and Fractions
5 7
x 
8 8
 x 5 7
8   8   8 
1 8 8
Multiply each term by 8
8x  5  7
Simplify
8x  5  5  7  5
Subtraction Property of Equality
8x  12
Simplify
12 3
1
x
  1  1.5
8 2
2
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) = 41
5.00h + 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