Solve 2/3(6x+5)-1/2=1.5(8-x)-11

$$\frac { 2 } { 3 } ( 6 x + 5 ) - \frac { 1 } { 2 } = 1.5 ( 8 - x ) - 11$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 6x+5.

$$\frac{2}{3}\times 6x+\frac{2}{3}\times 5-\frac{1}{2}=1.5\left(8-x\right)-11$$

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

$$\frac{2\times 6}{3}x+\frac{2}{3}\times 5-\frac{1}{2}=1.5\left(8-x\right)-11$$

Multiply 2 and 6 to get 12.

$$\frac{12}{3}x+\frac{2}{3}\times 5-\frac{1}{2}=1.5\left(8-x\right)-11$$

Divide 12 by 3 to get 4.

$$4x+\frac{2}{3}\times 5-\frac{1}{2}=1.5\left(8-x\right)-11$$

Express \frac{2}{3}\times 5 as a single fraction.

$$4x+\frac{2\times 5}{3}-\frac{1}{2}=1.5\left(8-x\right)-11$$

Multiply 2 and 5 to get 10.

$$4x+\frac{10}{3}-\frac{1}{2}=1.5\left(8-x\right)-11$$

Least common multiple of 3 and 2 is 6. Convert \frac{10}{3} and \frac{1}{2} to fractions with denominator 6.

$$4x+\frac{20}{6}-\frac{3}{6}=1.5\left(8-x\right)-11$$

Since \frac{20}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$4x+\frac{20-3}{6}=1.5\left(8-x\right)-11$$

Subtract 3 from 20 to get 17.

$$4x+\frac{17}{6}=1.5\left(8-x\right)-11$$

Use the distributive property to multiply 1.5 by 8-x.

$$4x+\frac{17}{6}=12-1.5x-11$$

Subtract 11 from 12 to get 1.

$$4x+\frac{17}{6}=1-1.5x$$

Add 1.5x to both sides.

$$4x+\frac{17}{6}+1.5x=1$$

Combine 4x and 1.5x to get 5.5x.

$$5.5x+\frac{17}{6}=1$$

Subtract \frac{17}{6} from both sides.

$$5.5x=1-\frac{17}{6}$$

Convert 1 to fraction \frac{6}{6}.

$$5.5x=\frac{6}{6}-\frac{17}{6}$$

Since \frac{6}{6} and \frac{17}{6} have the same denominator, subtract them by subtracting their numerators.

$$5.5x=\frac{6-17}{6}$$

Subtract 17 from 6 to get -11.

$$5.5x=-\frac{11}{6}$$

Divide both sides by 5.5.

$$x=\frac{-\frac{11}{6}}{5.5}$$

Express \frac{-\frac{11}{6}}{5.5} as a single fraction.

$$x=\frac{-11}{6\times 5.5}$$

Multiply 6 and 5.5 to get 33.

$$x=\frac{-11}{33}$$

Reduce the fraction \frac{-11}{33} to lowest terms by extracting and canceling out 11.

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