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

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

Solve for x

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$6\left(1+\frac{1}{2}\right)x+12=2\left(1-\frac{1}{2}\right)x+54$$

Convert 1 to fraction \frac{2}{2}.

$$6\left(\frac{2}{2}+\frac{1}{2}\right)x+12=2\left(1-\frac{1}{2}\right)x+54$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$6\times \frac{2+1}{2}x+12=2\left(1-\frac{1}{2}\right)x+54$$

Add 2 and 1 to get 3.

$$6\times \frac{3}{2}x+12=2\left(1-\frac{1}{2}\right)x+54$$

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

$$\frac{6\times 3}{2}x+12=2\left(1-\frac{1}{2}\right)x+54$$

Multiply 6 and 3 to get 18.

$$\frac{18}{2}x+12=2\left(1-\frac{1}{2}\right)x+54$$

Divide 18 by 2 to get 9.

$$9x+12=2\left(1-\frac{1}{2}\right)x+54$$

Convert 1 to fraction \frac{2}{2}.

$$9x+12=2\left(\frac{2}{2}-\frac{1}{2}\right)x+54$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$9x+12=2\times \frac{2-1}{2}x+54$$

Subtract 1 from 2 to get 1.

$$9x+12=2\times \frac{1}{2}x+54$$

Cancel out 2 and 2.

$$9x+12=x+54$$

Subtract x from both sides.

$$9x+12-x=54$$

Combine 9x and -x to get 8x.

$$8x+12=54$$

Subtract 12 from both sides.

$$8x=54-12$$

Subtract 12 from 54 to get 42.

$$8x=42$$

Divide both sides by 8.

$$x=\frac{42}{8}$$

Reduce the fraction \frac{42}{8} to lowest terms by extracting and canceling out 2.

$$x=\frac{21}{4}$$