#
Section 1-3

#
Solving Multi-Step Equations

Most often, you need two operations to solve a
linear equation
. In this case,
you usually need to add or subtract first (to get the variable alone with a
coefficient), and then multiply or divide. This is because you're basically
doing the
order of operations
in
reverse to get back to the variable.

**
Example 1:
**

Solve for
*
x
*
:

**
3
***
x
*
+ 5 = 11

First, subtract 5 from each side to get a constant on the right.

**
3
***
x
*
+ 5 – 5 = 11 – 5

**
3
***
x
*
= 6

Now divide both sides by 3 to isolate the
*
x
*
.

**
***
x
*
= 2
**
**

**
Example 2:
**

Solve for
*
x
*
:

First add 8 to both sides to get a constant on the right.

Then multiply both sides by the
reciprocal
of
**
–
**
7/2, which is
**
–
**
2/7, to isolate the
*
x
*
.

**
***
x
*
= 4

Again, we've
*
solved the equation
*
.