Question

Andrew knows that exactly two of the equations $x(3+4)=4(x+3),$ $4x+5=3(x+2),$ and $(x+2)+5(x-1)=3(x+3)$ are true. What is the value of $x?$

Answer 1

`4`

Explanation:

The equations are

`x(3+4)=4(x+3)\\\Rightarrow 7x=4x+12\\\Rightarrow x=(12)/(7-4)\\\Rightarrow x=4`

`4x+5=3(x+2)\\\Rightarrow 4x+5=3x+6\\\Rightarrow x=1`

`(x+2)+5(x-1)=3(x+3)\\\Rightarrow x+2+5x-5=3x+9\\\Rightarrow 6x-3=3x+9\\\Rightarrow 3x=12\\\Rightarrow x=4`

The two equations that are true are
`x(3+4)=4(x+3)` and
`(x+2)+5(x-1)=3(x+3)` and the value of
`x` is
`4`.