Question

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

Answer 1

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-8

Distribute 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-8

Let's first solve:

2x-14=x-8

Subtract x on both sides:

x-14=-8

Add 14 on both sides:

x=-8+14

Simplify:

x=6

Let's solve:

-(2x-14)=x-8

Distribute:

-2x+14=x-8

Add 2x on both sides:

14=3x-8

Add 8 on both sides:

22=3x

Divide both sides by 3:

22/3=x

So let's check both x=6 and x=22.3.

2|x-7|=x-8 for x=6:

2|6-7|=6-8

2|-1|=-2

2(1)=-2

2=-2 is not true so x=6 is extraneous.

2|x-7|=x-8 for x=22/3:

2|22/3-7|=22/3-8

2|22/3-21/3|=22/3-24/3

2|1/3|=-2/3

2/3=-2/3 is not true so x=22/3 is extraneous.