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

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

Solve for k

$$k=-\frac{13x}{9}-2$$

Steps for Solving Linear Equation

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

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

Add 5 and 1 to get 6.

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

Subtract \frac{2}{3}x from both sides.

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

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

$$-3k=\frac{13}{3}x+6$$

The equation is in standard form.

$$-3k=\frac{13x}{3}+6$$

Divide both sides by -3.

$$\frac{-3k}{-3}=\frac{\frac{13x}{3}+6}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$k=\frac{\frac{13x}{3}+6}{-3}$$

Divide \frac{13x}{3}+6 by -3.

$$k=-\frac{13x}{9}-2$$

Solve for x

$$x=\frac{-9k-18}{13}$$

Steps for Solving Linear Equation

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

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

Add 5 and 1 to get 6.

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

Subtract 5x from both sides.

$$\frac{2}{3}x-3k-5x=6$$

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

$$-\frac{13}{3}x-3k=6$$

Add 3k to both sides.

$$-\frac{13}{3}x=6+3k$$

The equation is in standard form.

$$-\frac{13}{3}x=3k+6$$

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

$$\frac{-\frac{13}{3}x}{-\frac{13}{3}}=\frac{3k+6}{-\frac{13}{3}}$$

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

$$x=\frac{3k+6}{-\frac{13}{3}}$$

Divide 6+3k by -\frac{13}{3} by multiplying 6+3k by the reciprocal of -\frac{13}{3}.

$$x=\frac{-9k-18}{13}$$