Solve x=4/7(y+z)

$$x = \frac { 4 } { 7 } ( y + z )$$

Solve for y

$$y=\frac{7x}{4}-z$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{7} by y+z.

$$x=\frac{4}{7}y+\frac{4}{7}z$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{4}{7}y+\frac{4}{7}z=x$$

Subtract \frac{4}{7}z from both sides.

$$\frac{4}{7}y=x-\frac{4}{7}z$$

The equation is in standard form.

$$\frac{4}{7}y=-\frac{4z}{7}+x$$

Divide both sides of the equation by \frac{4}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{7}y}{\frac{4}{7}}=\frac{-\frac{4z}{7}+x}{\frac{4}{7}}$$

Dividing by \frac{4}{7} undoes the multiplication by \frac{4}{7}.

$$y=\frac{-\frac{4z}{7}+x}{\frac{4}{7}}$$

Divide x-\frac{4z}{7} by \frac{4}{7} by multiplying x-\frac{4z}{7} by the reciprocal of \frac{4}{7}.

$$y=\frac{7x}{4}-z$$

Solve for x

$$x=\frac{4\left(y+z\right)}{7}$$

Solution Steps

Use the distributive property to multiply \frac{4}{7} by y+z.

$$x=\frac{4}{7}y+\frac{4}{7}z$$