#### 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.

Problem 3.4b:

Isolate the absolute value term.

Either or

Solve

Solve

The answers are 4.1712927296,-1.83795939622, 2.77485177345 and -1.44151844011. These answers may or may not be solutions to the original equation. You must verify each of the answers.

Check x=4.1712927296 by substituting 4.1712927296 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 is equal to the right side of the original equation, the answer x= 4.1712927296 is a solution to the original equation.

Check x=-1.83795939622 by substituting -1.83795939622 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 is not equal to the right side of the original equation, the answer x=-1.83795939622 is not a solution to the original equation.

Check x=2.77485177345 by substituting 2.77485177345 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 is equal to the right side of the original equation, the answer x=2.77485177345 is a solution to the original equation.

Check x=-1.44151844011 by substituting -1.44151844011 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 is equal to the right side of the original equation, the answer x=-1.44151844011 is a solution to the original equation.

The solutions are 4.1712927296, -1.44151844011 , and 2.77485177345.

on your graphing calculator. The graph was formed by subtracting the right side of the original equation from the left side of the original equation. You will note that the three x-intercepts on the graph are located at x=4.1712927296, -1.44151844011 ,and 2.77485177345. This verifies the three solutions by a graphical method.

If you would like to review the solution to problem 3.4c, click on Solution

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

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