Solve 5/8(x-16)=4x+2

$$\frac { 5 } { 8 } ( x - 16 ) = 4 x + 2$$

Solve for x

$$x = -\frac{32}{9} = -3\frac{5}{9} \approx -3.555555556$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{8} by x-16.

$$\frac{5}{8}x+\frac{5}{8}\left(-16\right)=4x+2$$

Express \frac{5}{8}\left(-16\right) as a single fraction.

$$\frac{5}{8}x+\frac{5\left(-16\right)}{8}=4x+2$$

Multiply 5 and -16 to get -80.

$$\frac{5}{8}x+\frac{-80}{8}=4x+2$$

Divide -80 by 8 to get -10.

$$\frac{5}{8}x-10=4x+2$$

Subtract 4x from both sides.

$$\frac{5}{8}x-10-4x=2$$

Combine \frac{5}{8}x and -4x to get -\frac{27}{8}x.

$$-\frac{27}{8}x-10=2$$

Add 10 to both sides.

$$-\frac{27}{8}x=2+10$$

Add 2 and 10 to get 12.

$$-\frac{27}{8}x=12$$

Multiply both sides by -\frac{8}{27}, the reciprocal of -\frac{27}{8}.

$$x=12\left(-\frac{8}{27}\right)$$

Express 12\left(-\frac{8}{27}\right) as a single fraction.

$$x=\frac{12\left(-8\right)}{27}$$

Multiply 12 and -8 to get -96.

$$x=\frac{-96}{27}$$

Reduce the fraction \frac{-96}{27} to lowest terms by extracting and canceling out 3.

$$x=-\frac{32}{9}$$