Question

Why does |7 + 3x| = x -1 have no solution? I could plug in, for example 5, and the answer would be positive.


Thank you =)

Answer 1

you might plug in x = 5, but x=5 does not satisfy the equation, so it is not a solution. So what if both sides are positive.
We know by definition that x-1 > 0 or
x>= 1
7+3x = x-1 or -7-3x = x-1
2x = -8 or -4x = 6
x = -4 or x = -3/2

subbing either one of these does not satisfy the equation, thus no solution
or

we established that x >= 1
and neither of the solutions satisfy this original condition, so there is no solution

Answer 2

Thanks. That cleared up a lot of thinfs