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

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{3}\left(-4\right) as a single fraction.

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

Multiply 2 and -4 to get -8.

$$\frac{2}{3}x+\frac{-8}{3}+x=4$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{2}{3}x-\frac{8}{3}+x=4$$

Combine \frac{2}{3}x and x to get \frac{5}{3}x.

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

Add \frac{8}{3} to both sides.

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

Convert 4 to fraction \frac{12}{3}.

$$\frac{5}{3}x=\frac{12}{3}+\frac{8}{3}$$

Since \frac{12}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}x=\frac{12+8}{3}$$

Add 12 and 8 to get 20.

$$\frac{5}{3}x=\frac{20}{3}$$

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

$$x=\frac{20}{3}\times \frac{3}{5}$$

Multiply \frac{20}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{20\times 3}{3\times 5}$$

Cancel out 3 in both numerator and denominator.

$$x=\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$x=4$$