Solve y-4=-6/7left(x+5right)

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

Solve for x

$$x=-\frac{7y}{6}-\frac{1}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{6}{7} by x+5.

$$y-4=-\frac{6}{7}x-\frac{30}{7}$$

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

$$-\frac{6}{7}x-\frac{30}{7}=y-4$$

Add \frac{30}{7} to both sides.

$$-\frac{6}{7}x=y-4+\frac{30}{7}$$

Add -4 and \frac{30}{7} to get \frac{2}{7}.

$$-\frac{6}{7}x=y+\frac{2}{7}$$

Divide both sides of the equation by -\frac{6}{7}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{6}{7}x}{-\frac{6}{7}}=\frac{y+\frac{2}{7}}{-\frac{6}{7}}$$

Dividing by -\frac{6}{7} undoes the multiplication by -\frac{6}{7}.

$$x=\frac{y+\frac{2}{7}}{-\frac{6}{7}}$$

Divide y+\frac{2}{7} by -\frac{6}{7} by multiplying y+\frac{2}{7} by the reciprocal of -\frac{6}{7}.

$$x=-\frac{7y}{6}-\frac{1}{3}$$

Solve for y

$$y=\frac{-6x-2}{7}$$

Solution Steps

Use the distributive property to multiply -\frac{6}{7} by x+5.

$$y-4=-\frac{6}{7}x-\frac{30}{7}$$

Add 4 to both sides.

$$y=-\frac{6}{7}x-\frac{30}{7}+4$$

Add -\frac{30}{7} and 4 to get -\frac{2}{7}.

$$y=-\frac{6}{7}x-\frac{2}{7}$$