How do you solve abs(x-5)= 5 ?

2 Answers
Mar 3, 2018

The solutions are x=0,10.

Explanation:

There are two possible solutions to an absolute value equation.

For example, the solutions for |x|=1 are x=1 and x=-1, because the absolute values of 1 and -1 are both 1.

The equation |x-5|=5 splits into to solutions: x-5=5 and x-5=-5. Now, solve for x in both of the new equations.

qquadqquadqquadqquad|x-5|=5
" ↙ ↘"
color(white){color(black)( (x-5=5, qquadqquad x-5=-5), (x=10, qquadqquad x=0)):}

Those are the two solutions. We can verify them by plugging them into the original equation:

|x-5|=5

Check 0:

|0-5|=5

|-5|=5

5=5" "sqrt

The solution 0 works. Check 10:

|10-5|=5

|5|=5

5=5" "sqrt

The solution 10 also works, so both solutions are correct. Hope this helps.

Mar 3, 2018

x=0 or 10

Explanation:

x-5 =5 or x-5=-5
x=5+5 or x=-5+5
x=10 or x=0