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:
3x + 5 = 11
First, subtract 5 from each side to get a constant on the right.
3x + 5 – 5 = 11 – 5
3x = 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.
