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

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

Solve for x

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x+2.

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

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

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

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

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

Divide -2 by 2 to get -1.

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

Subtract \frac{1}{2}x from both sides.

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

Combine 3x and -\frac{1}{2}x to get \frac{5}{2}x.

$$\frac{5}{2}x+6=-1$$

Subtract 6 from both sides.

$$\frac{5}{2}x=-1-6$$

Subtract 6 from -1 to get -7.

$$\frac{5}{2}x=-7$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$x=-7\times \frac{2}{5}$$

Express -7\times \frac{2}{5} as a single fraction.

$$x=\frac{-7\times 2}{5}$$

Multiply -7 and 2 to get -14.

$$x=\frac{-14}{5}$$

Fraction \frac{-14}{5} can be rewritten as -\frac{14}{5} by extracting the negative sign.

$$x=-\frac{14}{5}$$