Find the extraneous solution of the equation |2x−10|=−3x

Question

Find the extraneous solution of the equation |2x−10|=−3x

Answer 1

An absolute value I 2x -10 I = -3x has 2 solutions. When solving an absolute value problem, it is necessary to create 2 separate equations. In this case, however, no absolute value can be negative.

2x - 10 = -3x 2x - 10 = 3x Solve each:

-10 = -5x -10 = 1x

2 = x x = -10 Check each solution to find the extraneous answer.

when x = 2, (2)(2) - 10 = (-3)(2) when x = -10, (2)(-10) -10 = (3)(10)

4 - 10 = -6 - 20 - 10 = 30

-30 does not equal 30, so -10 is the

extraneous value.