Solve (4/3-2/3x)*2+3x=6

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3}-\frac{2}{3}x by 2.

$$\frac{4}{3}\times 2-\frac{2}{3}x\times 2+3x=6$$

Express \frac{4}{3}\times 2 as a single fraction.

$$\frac{4\times 2}{3}-\frac{2}{3}x\times 2+3x=6$$

Multiply 4 and 2 to get 8.

$$\frac{8}{3}-\frac{2}{3}x\times 2+3x=6$$

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

$$\frac{8}{3}+\frac{-2\times 2}{3}x+3x=6$$

Multiply -2 and 2 to get -4.

$$\frac{8}{3}+\frac{-4}{3}x+3x=6$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{8}{3}-\frac{4}{3}x+3x=6$$

Combine -\frac{4}{3}x and 3x to get \frac{5}{3}x.

$$\frac{8}{3}+\frac{5}{3}x=6$$

Subtract \frac{8}{3} from both sides.

$$\frac{5}{3}x=6-\frac{8}{3}$$

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

$$\frac{5}{3}x=\frac{18}{3}-\frac{8}{3}$$

Since \frac{18}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}x=\frac{18-8}{3}$$

Subtract 8 from 18 to get 10.

$$\frac{5}{3}x=\frac{10}{3}$$

Multiply both sides by \frac{3}{5}, the reciprocal of \frac{5}{3}.

$$x=\frac{10}{3}\times \frac{3}{5}$$

Multiply \frac{10}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{10\times 3}{3\times 5}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$x=2$$