How do you solve #abs(x-10)=17#?
2 Answers
Explanation:
With absolute value equations, you need to evaluate both negative and positive circumstances of the absolute value.
AND
[We ignore the absolute value sign until we check our answers]
So,
AND
Therefore, our two values for
I'll check them below for reference.
[Remember to substitute your values only into the original equation!]
OR
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"#