Luttrell 2012
26
Name: ______________________
Date: _____
2j-Solving for a Variable (multiple steps)
When solving for a variable, reverse the order of operations. The objective is to isolate that
variable by getting it to one side of the equation and all the constants to the other side. If faced
with an equation with a nested variable (see example C), eliminate the outer portion before
messing with the interior of an expression. To eliminate terms or coefficients, you will need to
apply the inverse operations.
Examples:
A. 3
x
= 24
B. 3
x
+ 1 = 25
C. (3
x
-1) ÷ 5 = 3
(3
x
)÷3 = 24÷3
3
x
+1 -1 = 25 - 1
(3
x
-1)÷5×5 = 3×5
x
= 8
3
x
= 24 3
x
- 1 = 15
3
3
24
3
x
=
3
x
-1 + 1 = 15 + 1
x
= 8 3
x
= 16
3
3
16
3
x
=
x
= 5⅓
Solve for the variable in the following equations:
1. 3
x
- 4 = 11
2. 5
x
+ 7 = - 3
3. -3
x
+ 2 = 17
4.
2
3
3
5
x
+
=
5.
2
5
2
3
x
+
=
6. 2(2
x
- 1) = 8
*7.
2
5
2
3
3
x
+
− =
*8.
3
2
3
7
6
x
+
+ =
*9. 3(
x
+5) - 2 = 7