Solve for: (1)/(4) * (x+1)=3(1-x)+(1)/(2)x

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

Multiply both sides of the equation by $4$

$x+1=12\left( 1-x \right)+2x$

Distribute $12$ through the parentheses

$x+1=12-12x+2x$

Collect like terms

$x+1=12-10x$

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

$x+1+10x=12$

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

$x+10x=12-1$

Collect like terms

$11x=12-1$

Subtract the numbers

$11x=11$

Divide both sides of the equation by $11$

$x=1$