Solve 4/5(4n-2)=-2/3(n+3)

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

Solve for n

$$n=-\frac{3}{29}\approx -0.103448276$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{5} by 4n-2.

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

Express \frac{4}{5}\times 4 as a single fraction.

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

Multiply 4 and 4 to get 16.

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

Express \frac{4}{5}\left(-2\right) as a single fraction.

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

Multiply 4 and -2 to get -8.

$$\frac{16}{5}n+\frac{-8}{5}=-\frac{2}{3}\left(n+3\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{16}{5}n-\frac{8}{5}=-\frac{2}{3}\left(n+3\right)$$

Use the distributive property to multiply -\frac{2}{3} by n+3.

$$\frac{16}{5}n-\frac{8}{5}=-\frac{2}{3}n-\frac{2}{3}\times 3$$

Cancel out 3 and 3.

$$\frac{16}{5}n-\frac{8}{5}=-\frac{2}{3}n-2$$

Add \frac{2}{3}n to both sides.

$$\frac{16}{5}n-\frac{8}{5}+\frac{2}{3}n=-2$$

Combine \frac{16}{5}n and \frac{2}{3}n to get \frac{58}{15}n.

$$\frac{58}{15}n-\frac{8}{5}=-2$$

Add \frac{8}{5} to both sides.

$$\frac{58}{15}n=-2+\frac{8}{5}$$

Convert -2 to fraction -\frac{10}{5}.

$$\frac{58}{15}n=-\frac{10}{5}+\frac{8}{5}$$

Since -\frac{10}{5} and \frac{8}{5} have the same denominator, add them by adding their numerators.

$$\frac{58}{15}n=\frac{-10+8}{5}$$

Add -10 and 8 to get -2.

$$\frac{58}{15}n=-\frac{2}{5}$$

Multiply both sides by \frac{15}{58}, the reciprocal of \frac{58}{15}.

$$n=-\frac{2}{5}\times \frac{15}{58}$$

Multiply -\frac{2}{5} times \frac{15}{58} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{-2\times 15}{5\times 58}$$

Do the multiplications in the fraction \frac{-2\times 15}{5\times 58}.

$$n=\frac{-30}{290}$$

Reduce the fraction \frac{-30}{290} to lowest terms by extracting and canceling out 10.

$$n=-\frac{3}{29}$$