How do you solve #abs(x-10)=17#?

2 Answers
Apr 24, 2017

Answer:

#x=27,-7#

Explanation:

With absolute value equations, you need to evaluate both negative and positive circumstances of the absolute value.

#|x-10|=17#

AND

#|x-10|=-17#

[We ignore the absolute value sign until we check our answers]

So,

#x-10=17#

#x=17+10#

#x=27#

AND

#x-10=-17#

#x=-17+10#

#x=-7#

Therefore, our two values for #x# are #27# and #-7#

I'll check them below for reference.
[Remember to substitute your values only into the original equation!]

#|x-10|=17#

#|27-10|=17#

#|17|=17#

#17=17#

OR

#|x-10|=17#

#|-7-10|=17#

#|-17|=17#

#17=17#

Apr 24, 2017

Answer:

#x=-7" or " x=27#

Explanation:

The value inside the #color(blue)"absolute value function"# can be positive or negative. This means there are 2 possible solutions.

#|x=10|=17#

#rArrx-10=color(red)(+-)17#

#(1)" solve " x-10=color(red)(+)17#

#"add 10 to both sides"#

#xcancel(-10)cancel(+10)=17+10#

#rArrx=27" is a possible solution"#

#(2)" solve " x-10=color(red)(-)17#

#"add 10 to both sides"#

#rArrx=-17+10#

#rArrx=-7" is a possible solution"#

#color(blue)"As a check"#

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#"left side "=|27-10|=|17|=17=" right side"#

#"left side "=|-7-10|=|-17|=17=" right side"#

#rArrx=-7" or " x=27" are the solutions"#