Solve 1/2(x+3)=2x+6

$$\frac { 1 } { 2 } ( x + 3 ) = 2 x + 6$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

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

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

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

Subtract 2x from both sides.

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

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

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

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

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

Convert 6 to fraction \frac{12}{2}.

$$-\frac{3}{2}x=\frac{12}{2}-\frac{3}{2}$$

Since \frac{12}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}x=\frac{12-3}{2}$$

Subtract 3 from 12 to get 9.

$$-\frac{3}{2}x=\frac{9}{2}$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=\frac{9}{2}\left(-\frac{2}{3}\right)$$

Multiply \frac{9}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{9\left(-2\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{9\left(-2\right)}{2\times 3}.

$$x=\frac{-18}{6}$$

Divide -18 by 6 to get -3.

$$x=-3$$