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```Multi-Step Equations
Table of
Contents
Steps for Solving Multiple Step Equations
As equations become more complex, you should:
1. Simplify each side of the equation.
(Combining like terms and the distributive property)
2. Use inverse operations to solve the equation.
Remember, whatever you do to one side of an equation,
you MUST do to the other side!
Examples:
-15 = -2x - 9 + 4x
-15 = 2x - 9
Combine Like Terms
+9
+9
Undo Subtraction first
-6 = 2x
2 2
Undo Multiplication second
-3 = x
7x - 3x - 8 = 24
4x - 8 = 24
Combine Like Terms
+ 8 +8
Undo Subtraction first
4x = 32
4
4
Undo Multiplication second
x=8
Now try an example. Each term is infinitely cloned
so you can pull them down as you solve.
-7x
+ 3 + 6x
= -6
ans
wer
Now try another example. Each term is infinitely cloned
so you can pull them down as you solve.
6x
-5
+ x = 44
ans
wer
Always check to see that both sides of the equation are
simplified before you begin solving the equation.
Sometimes, you need to use the distributive property in order to
simplify part of the equation.
Distributive Property
For all real numbers a, b, c
a(b + c) = ab + ac
a(b - c) = ab - ac
Examples
5(20 + 6) = 5(20) + 5(6)
9(30 - 2) = 9(30) - 9(2)
3(5 + 2x) = 3(5) + 3(2x)
-2(4x - 7) = -2(4x) - (-2)(7)
Examples:
5(1 + 6x) = 185
5 + 30x = 185 Distribute the 5 on the left side
-5
-5
30xMove
30
30
Undo multiplication second
x=6
2x + 6(x - 3) = 14
2x + 6x - 18 = 14
Distribute the 6 through (x - 3)
8x - 18 = 14
Combine Like Terms
+18 +18
Undo subtraction
8x = 32
8
8
Undo multiplication
x=4
Now show the distributing and solve
5 ( -2 + 7x ) = 95
Now show the distributing and solve
6 ( -2x + 9 ) = 102
23
Solve.
3 + 2t + 4t = -63
24
Solve.
19 = 1 + 4 - x
25
Solve.
8x - 4 - 2x - 11 = -27
26
Solve.
-4 = -27y + 7 - (-15y) + 13
27
Solve.
9 - 4y + 16 + 11y = 4
28
Solve.
6(-8 + 3b) = 78
29
Solve.
18 = -6(1 - 1k)
30
Solve.
2w + 8(w + 3) = 34
31
Solve.
4 = 4x - 2(x + 6)
32
Solve.
3r - r + 2(r + 4) = 24
33
What is the value of p in the equation
2(3p - 4) = 10?
A
B
C
D
1
2 1/3
3
1/3
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17,
June, 2011.
```
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