Solve 2/3x-1=6m+5(x-m)

$$\frac { 2 } { 3 } x - 1 = 6 m + 5 ( x - m )$$

Solve for m

$$m=-\frac{13x}{3}-1$$

Solution Steps

Use the distributive property to multiply 5 by x-m.

$$\frac{2}{3}x-1=6m+5x-5m$$

Combine 6m and -5m to get m.

$$\frac{2}{3}x-1=m+5x$$

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

$$m+5x=\frac{2}{3}x-1$$

Subtract 5x from both sides.

$$m=\frac{2}{3}x-1-5x$$

Combine \frac{2}{3}x and -5x to get -\frac{13}{3}x.

$$m=-\frac{13}{3}x-1$$

Solve for x

$$x=\frac{-3m-3}{13}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-m.

$$\frac{2}{3}x-1=6m+5x-5m$$

Combine 6m and -5m to get m.

$$\frac{2}{3}x-1=m+5x$$

Subtract 5x from both sides.

$$\frac{2}{3}x-1-5x=m$$

Combine \frac{2}{3}x and -5x to get -\frac{13}{3}x.

$$-\frac{13}{3}x-1=m$$

Add 1 to both sides.

$$-\frac{13}{3}x=m+1$$

Divide both sides of the equation by -\frac{13}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{13}{3}x}{-\frac{13}{3}}=\frac{m+1}{-\frac{13}{3}}$$

Dividing by -\frac{13}{3} undoes the multiplication by -\frac{13}{3}.

$$x=\frac{m+1}{-\frac{13}{3}}$$

Divide m+1 by -\frac{13}{3} by multiplying m+1 by the reciprocal of -\frac{13}{3}.

$$x=\frac{-3m-3}{13}$$