Solve 1/5(2n+1)=2/3(n-1)

$$\frac { 1 } { 5 } ( 2 n + 1 ) = \frac { 2 } { 3 } ( n - 1 )$$

Solve for n

$$n = \frac{13}{4} = 3\frac{1}{4} = 3.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by 2n+1.

$$\frac{1}{5}\times 2n+\frac{1}{5}=\frac{2}{3}\left(n-1\right)$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$\frac{2}{5}n+\frac{1}{5}=\frac{2}{3}\left(n-1\right)$$

Use the distributive property to multiply \frac{2}{3} by n-1.

$$\frac{2}{5}n+\frac{1}{5}=\frac{2}{3}n+\frac{2}{3}\left(-1\right)$$

Multiply \frac{2}{3} and -1 to get -\frac{2}{3}.

$$\frac{2}{5}n+\frac{1}{5}=\frac{2}{3}n-\frac{2}{3}$$

Subtract \frac{2}{3}n from both sides.

$$\frac{2}{5}n+\frac{1}{5}-\frac{2}{3}n=-\frac{2}{3}$$

Combine \frac{2}{5}n and -\frac{2}{3}n to get -\frac{4}{15}n.

$$-\frac{4}{15}n+\frac{1}{5}=-\frac{2}{3}$$

Subtract \frac{1}{5} from both sides.

$$-\frac{4}{15}n=-\frac{2}{3}-\frac{1}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{4}{15}n=-\frac{10}{15}-\frac{3}{15}$$

Since -\frac{10}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{15}n=\frac{-10-3}{15}$$

Subtract 3 from -10 to get -13.

$$-\frac{4}{15}n=-\frac{13}{15}$$

Multiply both sides by -\frac{15}{4}, the reciprocal of -\frac{4}{15}.

$$n=-\frac{13}{15}\left(-\frac{15}{4}\right)$$

Multiply -\frac{13}{15} times -\frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{-13\left(-15\right)}{15\times 4}$$

Do the multiplications in the fraction \frac{-13\left(-15\right)}{15\times 4}.

$$n=\frac{195}{60}$$

Reduce the fraction \frac{195}{60} to lowest terms by extracting and canceling out 15.

$$n=\frac{13}{4}$$