Solve 5/3(x-16)=4x+2

$$\frac { 5 } { 3 } ( x - 16 ) = 4 x + 2$$

Solve for x

$$x = -\frac{86}{7} = -12\frac{2}{7} \approx -12.285714286$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{3} by x-16.

$$\frac{5}{3}x+\frac{5}{3}\left(-16\right)=4x+2$$

Express \frac{5}{3}\left(-16\right) as a single fraction.

$$\frac{5}{3}x+\frac{5\left(-16\right)}{3}=4x+2$$

Multiply 5 and -16 to get -80.

$$\frac{5}{3}x+\frac{-80}{3}=4x+2$$

Fraction \frac{-80}{3} can be rewritten as -\frac{80}{3} by extracting the negative sign.

$$\frac{5}{3}x-\frac{80}{3}=4x+2$$

Subtract 4x from both sides.

$$\frac{5}{3}x-\frac{80}{3}-4x=2$$

Combine \frac{5}{3}x and -4x to get -\frac{7}{3}x.

$$-\frac{7}{3}x-\frac{80}{3}=2$$

Add \frac{80}{3} to both sides.

$$-\frac{7}{3}x=2+\frac{80}{3}$$

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

$$-\frac{7}{3}x=\frac{6}{3}+\frac{80}{3}$$

Since \frac{6}{3} and \frac{80}{3} have the same denominator, add them by adding their numerators.

$$-\frac{7}{3}x=\frac{6+80}{3}$$

Add 6 and 80 to get 86.

$$-\frac{7}{3}x=\frac{86}{3}$$

Multiply both sides by -\frac{3}{7}, the reciprocal of -\frac{7}{3}.

$$x=\frac{86}{3}\left(-\frac{3}{7}\right)$$

Multiply \frac{86}{3} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{86\left(-3\right)}{3\times 7}$$

Do the multiplications in the fraction \frac{86\left(-3\right)}{3\times 7}.

$$x=\frac{-258}{21}$$

Reduce the fraction \frac{-258}{21} to lowest terms by extracting and canceling out 3.

$$x=-\frac{86}{7}$$