Section 1.6 Absolute Value Equations
Example 1.6.1.
Example 1.6.2.
Example 1.6.3.
Example 1.6.4.
Example 1.6.5.
Now notice we have two equations to solve, each equation will give us a different solution. Both equations solve like any other two-step equation.
Example 1.6.6.
To get the absolute value alone we first need to get rid of the
Now we just solve these two remaining equations to find our solutions.
We now have our two solutions,
Example 1.6.7.
Notice the absolute value equals a negative number! This is impossible with absolute value. When this occurs we say there is no solution or
Example 1.6.8.
Notice the first equation is the positive possibility and has no significant difference other than the missing absolute value bars. The second equation considers the negative possibility. For this reason, we have a negative in front of the expression which will be distributed through the equation on the first step of solving. So, we solve both these equations as follows:
This gives us our two solutions,