**
SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)**

Note:

- if and only if
- if and only if
*a*+*b*= 3 or*a*+*b*= -3 - Step1:
Isolate the absolute value expression. - Step 2:
Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation. - Step 3:
Solve for the unknown in both equations. - Step 4:
Check your answer analytically or graphically.

Example 4 :

Step1:

Step 2:

Step 3:

**The answers are 7 and . These answers may
not be solutions to the equation. You must verify the answers.**

Step 4:

Check the answer *x*=7 by substituting 7 in the original equation for
x. If the left side of the equation equals the right side of the
equation after the substitution, you have found the correct answer:

- Left side: .
- Right side:
8.5

Since the left side of the original equation equals the right side of
the original equation after the value 7 is substituted for x, we have
verified the solution *x*=7.

Check the answer *x*=-9.8 by substituting -9.8 in the original
equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the
correct answer.

- Left side:
.
- Right side: 8.5

Since the left side of the original equation equals the right side of the original equation after the value -9.8 is substituted for x, we have verified the solution =-9.8.

You can also check you answer by graphing
(the left side of the
original equation minus the right side of the original equation). You
will note that the two x-intercepts on the graph are located at 7 and
-9.8.

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