Solve each equation. Check for extraneous solutions.2 | x-7 | = x-8

Accepted Solution

Answer:Both x=6 and x=22/3 are extraneous. There are no actual solutions to the given equation. The equation given was: 2|x-7|=x-8.Step-by-step explanation:2|x-7|=x-8Distribute the 2. We can do this because 2=|2|.|2x-14|=x-8|2x-14|=|-(2x-14)| holds since |1|=|-1|.This means we have the following two equations to solve:2x-14=x-8 or -(2x-14)=x-8Let's first solve:2x-14=x-8Subtract x on both sides:x-14=-8Add 14 on both sides:x=-8+14Simplify:x=6Let's solve:-(2x-14)=x-8Distribute:-2x+14=x-8Add 2x on both sides:14=3x-8Add 8 on both sides:22=3xDivide both sides by 3:22/3=xSo let's check both x=6 and x=22.3.2|x-7|=x-8 for x=6:2|6-7|=6-82|-1|=-22(1)=-22=-2 is not true so x=6 is extraneous.2|x-7|=x-8 for x=22/3:2|22/3-7|=22/3-82|22/3-21/3|=22/3-24/32|1/3|=-2/32/3=-2/3 is not true so x=22/3 is extraneous.