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

Answer:

$4$

Step-by-step explanation:

The equations are

$x(3+4)=4(x+3)\\\Rightarrow 7x=4x+12\\\Rightarrow x=\dfrac{12}{7-4}\\\Rightarrow x=4$

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

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

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 $4$.