Solve 1/2x+2=2/3(x+2)

$$\frac { 1 } { 2 } x + 2 = \frac { 2 } { 3 } ( x + 2 )$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and 2 to get 4.

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x+2=\frac{4}{3}$$

Subtract 2 from both sides.

$$-\frac{1}{6}x=\frac{4}{3}-2$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{1}{6}x=\frac{4}{3}-\frac{6}{3}$$

Since \frac{4}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}x=\frac{4-6}{3}$$

Subtract 6 from 4 to get -2.

$$-\frac{1}{6}x=-\frac{2}{3}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}.

$$x=-\frac{2}{3}\left(-6\right)$$

Express -\frac{2}{3}\left(-6\right) as a single fraction.

$$x=\frac{-2\left(-6\right)}{3}$$

Multiply -2 and -6 to get 12.

$$x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x=4$$