Solve 6(3/2x+1)=-9(1/3x-2)

$$6 ( \frac { 3 } { 2 } x + 1 ) = - 9 ( \frac { 1 } { 3 } x - 2 )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by \frac{3}{2}x+1.

$$6\times \frac{3}{2}x+6=-9\left(\frac{1}{3}x-2\right)$$

Express 6\times \frac{3}{2} as a single fraction.

$$\frac{6\times 3}{2}x+6=-9\left(\frac{1}{3}x-2\right)$$

Multiply 6 and 3 to get 18.

$$\frac{18}{2}x+6=-9\left(\frac{1}{3}x-2\right)$$

Divide 18 by 2 to get 9.

$$9x+6=-9\left(\frac{1}{3}x-2\right)$$

Use the distributive property to multiply -9 by \frac{1}{3}x-2.

$$9x+6=-9\times \frac{1}{3}x+18$$

Multiply -9 and \frac{1}{3} to get \frac{-9}{3}.

$$9x+6=\frac{-9}{3}x+18$$

Divide -9 by 3 to get -3.

$$9x+6=-3x+18$$

Add 3x to both sides.

$$9x+6+3x=18$$

Combine 9x and 3x to get 12x.

$$12x+6=18$$

Subtract 6 from both sides.

$$12x=18-6$$

Subtract 6 from 18 to get 12.

$$12x=12$$

Divide both sides by 12.

$$x=\frac{12}{12}$$

Divide 12 by 12 to get 1.

$$x=1$$