Question

can you help with this one? Solve the equation. (If there is no solution, enter NO SOLUTION.)
|x − 7| = |3x + 8|

Answer 1

you have to solve two separate equations, namely
\[x-7=3x+8\] and
\[x-7=-(3x+8)\]

Answer 2

in other words just remove absolute value signs for one equation, then for the next take the negative of one of the sides (doesn't matter which)

Answer 3

first one is easy enough
\[x-7=3x+8\][
\[-7-8=3x-x\]
\[-15=2x\]
\[x=-\frac{15}{2}\]

Answer 4

second one first distribute the minus sign to get
\[x-7=-3x-8\] then proceed as usual
\[x+3x=-8+7\]
\[4x=-1\]
\[x=-\frac{1}{4}\]

Answer 5

ok?

Answer 6

got it so. -1/4 is obviously the larger value

Answer 7

yes for sure