Solve 1/2(x+6)=4(x-2)

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

Solve for x

$$x = \frac{22}{7} = 3\frac{1}{7} \approx 3.142857143$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+6.

$$\frac{1}{2}x+\frac{1}{2}\times 6=4\left(x-2\right)$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$\frac{1}{2}x+\frac{6}{2}=4\left(x-2\right)$$

Divide 6 by 2 to get 3.

$$\frac{1}{2}x+3=4\left(x-2\right)$$

Use the distributive property to multiply 4 by x-2.

$$\frac{1}{2}x+3=4x-8$$

Subtract 4x from both sides.

$$\frac{1}{2}x+3-4x=-8$$

Combine \frac{1}{2}x and -4x to get -\frac{7}{2}x.

$$-\frac{7}{2}x+3=-8$$

Subtract 3 from both sides.

$$-\frac{7}{2}x=-8-3$$

Subtract 3 from -8 to get -11.

$$-\frac{7}{2}x=-11$$

Multiply both sides by -\frac{2}{7}, the reciprocal of -\frac{7}{2}.

$$x=-11\left(-\frac{2}{7}\right)$$

Express -11\left(-\frac{2}{7}\right) as a single fraction.

$$x=\frac{-11\left(-2\right)}{7}$$

Multiply -11 and -2 to get 22.

$$x=\frac{22}{7}$$