Solve x=4(1/3x+2/3)-5

$$x = 4 ( 1 / 3 x + 2 / 3 ) - 5$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by \frac{1}{3}x+\frac{2}{3}.

$$x=4\times \frac{1}{3}x+4\times \frac{2}{3}-5$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$x=\frac{4}{3}x+4\times \frac{2}{3}-5$$

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

$$x=\frac{4}{3}x+\frac{4\times 2}{3}-5$$

Multiply 4 and 2 to get 8.

$$x=\frac{4}{3}x+\frac{8}{3}-5$$

Convert 5 to fraction \frac{15}{3}.

$$x=\frac{4}{3}x+\frac{8}{3}-\frac{15}{3}$$

Since \frac{8}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{4}{3}x+\frac{8-15}{3}$$

Subtract 15 from 8 to get -7.

$$x=\frac{4}{3}x-\frac{7}{3}$$

Subtract \frac{4}{3}x from both sides.

$$x-\frac{4}{3}x=-\frac{7}{3}$$

Combine x and -\frac{4}{3}x to get -\frac{1}{3}x.

$$-\frac{1}{3}x=-\frac{7}{3}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$x=-\frac{7}{3}\left(-3\right)$$

Express -\frac{7}{3}\left(-3\right) as a single fraction.

$$x=\frac{-7\left(-3\right)}{3}$$

Multiply -7 and -3 to get 21.

$$x=\frac{21}{3}$$

Divide 21 by 3 to get 7.

$$x=7$$