Solve 5(4y-x)=5(y+1)-2(x-1/2)

$$5 ( 4 y - x ) = 5 ( y + 1 ) - 2 ( x - \frac { 1 } { 2 } )$$

Solve for x

$$x=5y-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 4y-x.

$$20y-5x=5\left(y+1\right)-2\left(x-\frac{1}{2}\right)$$

Use the distributive property to multiply 5 by y+1.

$$20y-5x=5y+5-2\left(x-\frac{1}{2}\right)$$

Use the distributive property to multiply -2 by x-\frac{1}{2}.

$$20y-5x=5y+5-2x+1$$

Add 5 and 1 to get 6.

$$20y-5x=5y+6-2x$$

Add 2x to both sides.

$$20y-5x+2x=5y+6$$

Combine -5x and 2x to get -3x.

$$20y-3x=5y+6$$

Subtract 20y from both sides.

$$-3x=5y+6-20y$$

Combine 5y and -20y to get -15y.

$$-3x=-15y+6$$

The equation is in standard form.

$$-3x=6-15y$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{6-15y}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{6-15y}{-3}$$

Divide -15y+6 by -3.

$$x=5y-2$$

Solve for y

$$y=\frac{x+2}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 4y-x.

$$20y-5x=5\left(y+1\right)-2\left(x-\frac{1}{2}\right)$$

Use the distributive property to multiply 5 by y+1.

$$20y-5x=5y+5-2\left(x-\frac{1}{2}\right)$$

Use the distributive property to multiply -2 by x-\frac{1}{2}.

$$20y-5x=5y+5-2x+1$$

Add 5 and 1 to get 6.

$$20y-5x=5y+6-2x$$

Subtract 5y from both sides.

$$20y-5x-5y=6-2x$$

Combine 20y and -5y to get 15y.

$$15y-5x=6-2x$$

Add 5x to both sides.

$$15y=6-2x+5x$$

Combine -2x and 5x to get 3x.

$$15y=6+3x$$

The equation is in standard form.

$$15y=3x+6$$

Divide both sides by 15.

$$\frac{15y}{15}=\frac{3x+6}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$y=\frac{3x+6}{15}$$

Divide 6+3x by 15.

$$y=\frac{x+2}{5}$$