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.

• 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.

Solve for x in the following equation.

Problem 3.2a :

Step1: Isolate the absolute value expression by adding 8 to both sides of the equation.

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

Step 3: Solve for x in both equations.

The answers are and -1.

Step 4: Check the solution 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: 3

Check the solution x = -1 by substituting -1 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: 3
  

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 -1.

If you would like to review the solution and answer to problem 3.2b, click on Solution.

If you would like to go back to the problem page, click on Problem.

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