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

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

Solve for x

$$x = -\frac{290}{9} = -32\frac{2}{9} \approx -32.222222222$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 2 to get 4.

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

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

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

Combine 4x and -3x to get x.

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

Calculate -\frac{4}{3} to the power of 3 and get -\frac{64}{27}.

$$x+24=6\left(-\frac{64}{27}\right)+6$$

Express 6\left(-\frac{64}{27}\right) as a single fraction.

$$x+24=\frac{6\left(-64\right)}{27}+6$$

Multiply 6 and -64 to get -384.

$$x+24=\frac{-384}{27}+6$$

Reduce the fraction \frac{-384}{27} to lowest terms by extracting and canceling out 3.

$$x+24=-\frac{128}{9}+6$$

Convert 6 to fraction \frac{54}{9}.

$$x+24=-\frac{128}{9}+\frac{54}{9}$$

Since -\frac{128}{9} and \frac{54}{9} have the same denominator, add them by adding their numerators.

$$x+24=\frac{-128+54}{9}$$

Add -128 and 54 to get -74.

$$x+24=-\frac{74}{9}$$

Subtract 24 from both sides.

$$x=-\frac{74}{9}-24$$

Convert 24 to fraction \frac{216}{9}.

$$x=-\frac{74}{9}-\frac{216}{9}$$

Since -\frac{74}{9} and \frac{216}{9} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-74-216}{9}$$

Subtract 216 from -74 to get -290.

$$x=-\frac{290}{9}$$