SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:

if and only if
if and only if a+b=3 or a+b=-3
Step 1:Isolate the absolute value expression.
Step2: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.

Solve for x in the following equation.

Example 2:

Step 1:The absolute value is already isolated.

Since and , 5x+7=3 or 5x+7=-3

Step 2:Set the quantity within the absolute value notation to

Step 3:Solve for x in the equation 5x+7=3

eqnarray35

Solve for x in the equation 5x+7=-3.

eqnarray40

The answers are and -2.

Step 4: Check the solutions because answers are not always valid solutions to the equation.

Check the solution x = by substituting 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:

Since the left side of the original equation after we substituted the value

for, the solution tex2html_wrap_inline142

is valid

Check the solution x = -2 by substituting -2 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:

Since the left side of the original equation after we substituted the value -2 for, the solution x=-2 is valid

You can also check your 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 and -2. this verifies our solutions graphically.

If you would like to work another example, click on Example

If you would like to test yourself by working some problems similar to this example, click on Problems

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