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11-2 Solving Multi-Step Equations
Warm Up
Solve.
1. 3x = 102
x = 34
2. y = 15 y = 225
15
3. z – 100 = 21 z = 121
4. 1.1 + 5w = 98.6 w = 19.5
11-2 Solving Multi-Step Equations
Learn to solve multi-step equations.
11-2 Solving Multi-Step Equations
To solve a multi-step equation, you
may have to simplify the equation first
by combining like terms or by using the
Distributive Property.
11-2 Solving Multi-Step Equations
Additional Example 1A: Solving Equations That
Contain Like Terms
Solve.
8x + 6 + 3x – 2 = 37
11x + 4 = 37
–4 –4
11x
= 33
11x = 33
11 11
x=3
Combine like terms.
Subtract 4 from both sides.
Divide both sides by 11.
11-2 Solving Multi-Step Equations
Additional Example 1B: Solving Equations That
Contain Like Terms
Solve.
4(x – 6) + 7 = 11
4(x – 6) + 7 = 11 Distributive Property
4(x) – 4(6) + 7 = 11
Simplify by multiplying:
4x – 24 + 7 = 11 4(x) = 4x and 4(6) = 24.
4x – 17 = 11 Simplify by adding: –24 + 7 = 17.
+ 17 +17 Add 17 to both sides.
4x = 28
4
4 Divide both sides by 4.
x=7
11-2 Solving Multi-Step Equations
Check It Out: Example 1
Solve.
9x + 5 + 4x – 2 = 42
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract 3 from both sides.
13x
= 39
13x = 39 Divide both sides by 13.
13 13
x=3
11-2 Solving Multi-Step Equations
Remember!
The least common denominator (LCD) is the
smallest number that each of the denominators
will divide into.
11-2 Solving Multi-Step Equations
Additional Example 2: Solving Equations That
Contain Fractions
Solve.
7x + x – 17 = 2
3
2
9
9
The LCD is 18.
Multiply both
17
7x
x
2
18
+ – 9 = 18
sides by 18.
9
2
3
7x
x
17
2 Distributive
18 9 + 18 2 – 18 9 = 18 3 Property.
()
(
()
)
()
()
()
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
11-2 Solving Multi-Step Equations
Additional Example 2 Continued
23x – 34 = 12
Combine like terms.
+ 34 + 34
23x
= 46
23x = 46
23 23
Add 34 to both sides.
x=2
Divide both sides by 23.