Evaluate: (1)/(7) * (x+4)=2x-6(3-x)-5

Expression: $\frac{ 1 }{ 7 } \times \left( x+4 \right)=2x-6\left( 3-x \right)-5$

Distribute $\frac{ 1 }{ 7 }$ through the parentheses

$\frac{ 1 }{ 7 }x+\frac{ 4 }{ 7 }=2x-6\left( 3-x \right)-5$

Distribute $-6$ through the parentheses

$\frac{ 1 }{ 7 }x+\frac{ 4 }{ 7 }=2x-18+6x-5$

Collect like terms

$\frac{ 1 }{ 7 }x+\frac{ 4 }{ 7 }=8x-18-5$

Calculate the difference

$\frac{ 1 }{ 7 }x+\frac{ 4 }{ 7 }=8x-23$

Move the variable to the left-hand side and change its sign

$\frac{ 1 }{ 7 }x+\frac{ 4 }{ 7 }-8x=-23$

Move the constant to the right-hand side and change its sign

$\frac{ 1 }{ 7 }x-8x=-23-\frac{ 4 }{ 7 }$

Calculate the difference

$-\frac{ 55 }{ 7 }x=-23-\frac{ 4 }{ 7 }$

Calculate the difference

$-\frac{ 55 }{ 7 }x=-\frac{ 165 }{ 7 }$

Multiply both sides of the equation by $-\frac{ 7 }{ 55 }$

$x=3$