#### 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 2: Either or Solve:   Solve   The answers are -0.25, -2, 1.4265 and -1.0515. These answers may or may not be solutions to the original equation. You must verify each of the answers.

Check the solutions:

Check the answer x = -0.25 by substituting -0.25 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=-0.25 is a solution to the original equation.

Check 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 is equal to the right side of the original equation, the answer x=-2 is a solution to the original equation.

Check x=1.4265 by substituting 1.4265 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=1.4265 is a solution to the original equation.

Check x=-1.0515 by substituting -1.0515 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 almost equal to the right side of the original equation, the answer x=-1.0515 is a solution to the original equation. Since we rounded the solution, the check will not be exact.

The solutions are x=-0.25,-2,1.4265,-1.0515.

You can also check your answer by graphing 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 four x-intercepts on the graph are located at x= -0.25, -2, 1.4265 and -1.0515. This verifies the four solutions by a graphical method.

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