Solve 2x/3+3/6(8-x)={left(-4/3right)}^2+1

$$\frac{ 2x }{ 3 } + \frac{ 3 }{ 6 } (8-x)= { \left(- \frac{ 4 }{ 3 } \right) }^{ 2 } +1$$

Solve for x

$$x = -\frac{22}{3} = -7\frac{1}{3} \approx -7.333333333$$

Steps for Solving Linear Equation

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

$$2\times 2x+3\left(8-x\right)=6\left(-\frac{4}{3}\right)^{2}+6$$

Multiply 2 and 2 to get 4.

$$4x+3\left(8-x\right)=6\left(-\frac{4}{3}\right)^{2}+6$$

Use the distributive property to multiply 3 by 8-x.

$$4x+24-3x=6\left(-\frac{4}{3}\right)^{2}+6$$

Combine 4x and -3x to get x.

$$x+24=6\left(-\frac{4}{3}\right)^{2}+6$$

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$x+24=6\times \frac{16}{9}+6$$

Express 6\times \frac{16}{9} as a single fraction.

$$x+24=\frac{6\times 16}{9}+6$$

Multiply 6 and 16 to get 96.

$$x+24=\frac{96}{9}+6$$

Reduce the fraction \frac{96}{9} to lowest terms by extracting and canceling out 3.

$$x+24=\frac{32}{3}+6$$

Convert 6 to fraction \frac{18}{3}.

$$x+24=\frac{32}{3}+\frac{18}{3}$$

Since \frac{32}{3} and \frac{18}{3} have the same denominator, add them by adding their numerators.

$$x+24=\frac{32+18}{3}$$

Add 32 and 18 to get 50.

$$x+24=\frac{50}{3}$$

Subtract 24 from both sides.

$$x=\frac{50}{3}-24$$

Convert 24 to fraction \frac{72}{3}.

$$x=\frac{50}{3}-\frac{72}{3}$$

Since \frac{50}{3} and \frac{72}{3} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{50-72}{3}$$

Subtract 72 from 50 to get -22.

$$x=-\frac{22}{3}$$