Question

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?

Answer 1

`\huge\boxed{f=g(x)\ \text{for}\ x=-(16)/(3)=-5(1)/(3)}`

Explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

`f(x)=g(x)\iff(1)/(2)x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\(1)/(2)x-2x=2x-2x+8\\\\-1(1)/(2)x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-(2\cdot1+1)/(2)x=8\\\\-(3)/(2)x=8\qquad\text{multiply both sides by}\ -(2)/(3)\\\\\left(-(2\!\!\!\!\diagup)/(3\!\!\!\!\diagup)\right)\left(-(3\!\!\!\!\diagup)/(2\!\!\!\!\diagup)x\right)=\left(-(2)/(3)\right)\cdot8\\\\x=-(2\cdot8)/(3)\\\\x=-(16)/(3)`