Given h(x)=x-4 and g(x)=-|x-3|+10, find the solution to the equation h(x)=g(x)

Answer 1

An equation has a 'solution' when the value of x satisfies the equality. That is, when

x-4 = -|x-2| + 10

x + |x+2| = 14

Either

x + (x+2) = 14

2x + 2 = 14

2x = 12

x = 6

or else

x - (x+2) = 14

-2 = 14 [This makes no sense, so it is not an answer.]