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Solving Multi-Step Equations7-2
Learn to solve multi-step equations.
Solving Multi-Step Equations7-2
To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.
Solving Multi-Step Equations7-2
Solve.
8x + 6 + 3x – 2 = 37
Additional Example 1A: Solving Equations That Contain Like Terms
11x + 4 = 37 Combine like terms. – 4 – 4 Subtract 4 from both sides.
11x = 33
x = 3
Divide both sides by 11.3311
11x11
=
Solving Multi-Step Equations7-2
Check
Additional Example 1A Continued
8x + 6 + 3x – 2 = 37
8(3) + 6 + 3(3) – 2 = 37?
24 + 6 + 9 – 2 = 37?
37 = 37?
Substitute 3 for x.
Solving Multi-Step Equations7-2
Solve.
4(x – 6) + 7 = 11
Additional Example 1B: Solving Equations That Contain Like Terms
4(x – 6) + 7 = 11 Distributive Property
+ 17 +17 Add 17 to both sides.
x = 7
Divide both sides by 4.4x = 28 4 4
4(x) – 4(6) + 7 = 11
4x – 24 + 7 = 11Simplify by multiplying: 4(x) = 4x and 4(6) = 24.
4x – 17 = 11 Simplify by adding: –24 + 7 = 17.
Solving Multi-Step Equations7-2
Solve.
9x + 5 + 4x – 2 = 42
Check It Out: Example 1
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract 3 from both sides.13x = 39
x = 3
Divide both sides by 13.3913
13x13
=
Solving Multi-Step Equations7-2
Check
Check It Out: Example 1 Continued
9x + 5 + 4x – 2 = 42
9(3) + 5 + 4(3) – 2 = 42?
27 + 5 + 12 – 2 = 42 ?
42 = 42?
Substitute 3 for x.
Solving Multi-Step Equations7-2
If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) of the fractions. This step results in an equation without fractions, which may be easier to solve.
Solving Multi-Step Equations7-2
The least common denominator (LCD) is the smallest number that each of the denominators will divide into.
Remember!
Solving Multi-Step Equations7-2
Solve.
+ – =
Additional Example 2: Solving Equations That Contain Fractions
23
The LCD is 18.
x 2
7x9
17 9
18( ) + 18( ) – 18( ) = 18( )7x9
x2
17 9
23
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
( ) ( )x2
23
7x9
17 918 + – = 18
Distributive Property.
Multiply both sides by 18.
Solving Multi-Step Equations7-2
Additional Example 2 Continued
23x = 46
= 23x23
4623 Divide both sides by 23.
x = 2
+ 34 + 34 Add 34 to both sides.
23x – 34 = 12 Combine like terms.
Solving Multi-Step Equations7-2
Additional Example 2 Continued
69
69=
?
Check
x 2
7x9
17 9
+ – = 23
23 Substitute 2 for x.7(2)
9 + – =(2) 2
17 9
?
23
149 + – =2
2 17 9
?
23
149 + – =
17 9
?1
The LCD is 9.69
149 + – =9
9 17 9
?
Solving Multi-Step Equations7-2
Solve.
+ = –
Check It Out: Example 2A
14
54
3n4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( )54
–1 4
3n4
4 + = 4
( ) ( ) ( )3n4
54
–1 44 + 4 = 4
3n + 5 = –1
Distributive Property.
Solving Multi-Step Equations7-2
Check It Out: Example 2A Continued
3n + 5 = –1 – 5 –5 Subtract 5 from both sides.
3n = –6
3n3
–6 3
= Divide both sides by 3.
n = –2
Solving Multi-Step Equations7-2
Solve.
+ – =
Check It Out: Example 2B
13
The LCD is 9.
x 3
5x9
13 9
9( ) + 9( )– 9( ) = 9( )5x9
x3
13 9
13
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.
( )x3
13
5x9
13 9 9 + – = 9( )
Distributive Property.
Multiply both sides by 9.
Solving Multi-Step Equations7-2
8x = 16
= 8x8
16 8 Divide both sides by 8.
x = 2
+ 13 + 13 Add 13 to both sides.
8x – 13 = 3 Combine like terms.
Check It Out: Example 2B Continued
Solving Multi-Step Equations7-2
39
39=
?
Check
x 3
5x9
13 9
+ – = 13
13 Substitute 2 for x.5(2)
9 + – =(2) 3
13 9
?
13
109 + – =2
3 13 9
?
The LCD is 9.39
109 + – =6
9 13 9
?
Check It Out: Example 2B Continued
Solving Multi-Step Equations7-2
Solve.
1. 6x + 3x – x + 9 = 33
2. 8(x + 2) + 5 = 29
3. + =
5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate?
Lesson Quiz
x = 1
x = 3
x = 2858
x8
33 8
6x 7
4. – =2x21
2521
$8.50
x = 1 916
