SOLVING EQUATION 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 3.4d:

Answer:-37.138357 and 1.375735

Either or

Solve

Solve

The answers are -0.8616428528,-37.1383571472, 1.3757351161 and -1.66144940181. 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=-0.8616428528 by substituting -0.8616428528 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=-0.8616428528 is not a solution to the original equation.

Check x=-37.1383571472 by substituting -37.1383571472 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=-37.1383571472 is a solution to the original equation.

Check x=1.3757351161 by substituting 1.3757351161 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=1.3757351161 is a solution to the original equation.

Check x=-1.66144940181 by substituting -1.66144940181 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=-1.66144940181 is not a solution to the original equation. You could also make the observation that the absolute value of a number cannot be negative, therefore no negative answer is valid.

The solutions are -37.1383571472 and 1.3757351161.

You can also check your answer by graphing the function

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 two x-intercepts on the graph are located at x=-37.1383571472 and 1.3757351161. This verifies the two solutions by a graphical method.

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