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

Note:

• if and only if

• if and only if a + b = 3 or a + b = - 3

• if any only if a + b = + (x + y) or a + b = - (x+ y)

Solve for x in the following equation.

Example 1:

Either or

Step 1: Solve

Step 2: Solve 2 x - 1 = -(4x + 3).

The answers are -2 and . These answers may or may not be the solutions.

Check the answer 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 equals the right side of the original equation after we substituted the value -2 for x, then x = -2 is a solution.

Check the answer 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 equals the right side of the original equation after we substituted the value , then is a solution.

The solutions are x = - 2 and

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 -2 and This verifies the solution graphically.

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

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