We need to solve the equation to find x
[tex]-3(x-6)+4(x+1)=7x-14[/tex]We will simplify the left side by multiply each bracket by the number before it
-3(x - 6) = -3(x) + -3(-6) = -3x + 18
4(x + 1) = 4(x) + 4(1) = 4x + 4
Now put them on the left side
[tex]-3x+18+4x+4=7x-14[/tex]Add the like terms on the left side
[tex]\begin{gathered} (-3x+4x)+(18+4)=7x-14 \\ x+22=7x-14 \end{gathered}[/tex]Now we will collect x on the right side and the numbers on the left side
Subtract x from both sides
[tex]\begin{gathered} x-x+22=7x-x-14 \\ 22=6x-14 \end{gathered}[/tex]Add 14 to both sides
[tex]\begin{gathered} 22+14=6x-14+14 \\ 36=6x \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{36}{6}=\frac{6x}{6} \\ 6=x \end{gathered}[/tex]The value of x is 6
