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LESSON 10-5
Warm Up
Lesson 10-5 Warm-Up
ALGEBRA READINESS
LESSON 10-5
Warm Up
Lesson 10-5 Warm-Up
ALGEBRA READINESS
“Solving Multi-Step Equations”
(10-5)
What are the steps for
solving a multi-step
equation?
Step 1: Clear the equation of fractions and decimals. You can clear
decimals by using the decimal that has the most digits after it and moving
all of the decimals that number of jumps to the right.
Example: 0.5a2 + 0.875 = 13.25
Since 0.875 is the greatest number of place values from the end (3),
jump all of the decimals 3 places to the right, so 0.5a2 + 0.875 = 13.25 is
the same as 500a2 + 875 = 13,250
•
•
•
Step 2: Use the Distributive Property to remove parenthesis if you can’t
simplify the problem within them.
Example: 4 (25) = 4 (20 + 5) = 4 • 20 + 4 • 5 = 80 + 20 = 100
Step 3: Combine like terms on each side.
Examples: 4x + 5x = 9x
8a – 5a = 3a
Step 4: “Undo” (since you’re working backwards) addition and
subtraction.
t – 7 + 7 = 20 + 7
Examples: 2x + 5 – 5 = 10 – 5
4
Step 5: Undo multiplication and division.
4 • t = 20
Examples: 2x = 10
• 4
1 4
2
2
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
Solve 2c + 2 + 3c = 12.
2c + 2 + 3c = 12
2c + 3c + 2 = 12
Commutative Property
Simplify.
5c + 2 = 12
–2 –2
Subtraction Property of Equality
5c + 0 = 10
5c
= 10
Simplify.
5c
5
= 10
5
1c
= 2
Use the Division Property of Equality to isolate
the variable (get the letter by itself).
Simplify.
1
1
Identity Property of Addition
2
1
Check 2c + 2 + 3c = 12
2(2) + 2 + 3(2) 12
12 = 12
Substitute 2 for c.
The solution checks.
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
Eight cheerleaders set a goal of selling 424 boxes of cards
to raise money. After two weeks, each cheerleader has sold 28
boxes. How many more boxes must each cheerleader sell?
Words
8 cheerleaders •
Let
Equation
8
28 boxes
per
cheerleader
additional
+ boxes per
= 424 boxes
cheerleader
x = the number of additional boxes.
•
(28
+
x)
=
424
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
(continued)
8(28 + x) = 424
8 • 28 + 8 • x = 424
224 +
– 224
0 +
8x = 424
– 224
Distributive Property
Simplify.
Use the Subtraction Property of Equality.
8x = 200
Simplify.
8x 200
=
8
8
Division Property of Equality
1 x = 25
Simplify.
Each cheerleader must sell 25 more boxes.
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
Solve 3a + 6 + a = 90
4a + 6 = 90
-6 - 6
Combine like terms (3a + 1a).
4a
Simplify.
= 84
4a + 0 = 84
4
4
1 a = 21
Divide each side by 4.
Simplify.
Check: 3a + 6 + a = 90
3(21) + 6 + 21
90
63 + 6 + 21
90
Substitute 21 for a.
90 = 90
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
Solve 3x + x = 17
2
5
Method 1: Finding common denominators
3x
x
+
2
5
3
1
x
+
2
5x
15
2
x
+
10
10 x
17
10 x
1
1
= 17
= 17
Rewrite the equation.
= 17
A common denominator of 2 and 5 is 10.
= 17
Combine like terms.
3
1
10 ( 17 x) = 17 ( 10 )
17 10
1 17
1
1
1
1 x = 10
1
Multiply each side by the reciprocal
of 17 , which is 10 .
10
17
Simplify.
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
(continued)
Method 2: Multiply both sides by the common denominator to clear the fractions.
3x x
+ = 17
2
5
3x x
10( 2 + 5 ) = 10(17)
Multiply each side by 10, a common
multiple of 2 and 5.
2
5
10 3x
10 ( x ) = 10( 17 )
(
)
+
1 1
1 2
1 5
1
1
15x
Use the Distributive Property.
+
17x
2x
= 170
Simplify.
= 170
Combine like terms.
17x
170
=
17
17
Divide each side by 17 to isolate the x.
1 x = 10
Simplify.
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Additional Examples
Solve 0.6a + 18.65 = 22.85.
0•6 0• a + 18•65• = 22•85•
60a + 1865 = 2285
- 1865 - 1865
60a + 0 = 420
60a
60 =
420
60
The greatest number of decimal
places is two places, so move
each decimal two places to right.
Simplify.
Subtract 1865 from each side.
Simplify.
Divide each side by 60 to isolate
the a.
1a =
7
Simplify.
ALGEBRA READINESS
Solving Multi-Step Equations
LESSON 10-5
Lesson Quiz
Solve the following equations.
1. 2m + 4 – 8m = 28
m = –4
2. 2(f – 1) + f = 37
f = 13
3. 4.5(4x – 12) = 144
x = 11
4. Jasmine earns a certain amount per hour for the first 40 hours worked in a
week. Each hour she works over 40 in one week, she earns an additional
$4.50 per hour. If Jasmine works 46 hours one week and earns $383.50
that week, how much does she earn per hour for the first 40 hours?
$7.75 per hour
ALGEBRA READINESS