Solve 4(k-1)+4/5(k+1)=1/4(2k+3)

$$4 ( k - 1 ) + \frac { 4 } { 5 } ( k + 1 ) = \frac { 1 } { 4 } ( 2 k + 3 )$$

Solve for k

$$k=\frac{79}{86}\approx 0.918604651$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by k-1.

$$4k-4+\frac{4}{5}\left(k+1\right)=\frac{1}{4}\left(2k+3\right)$$

Use the distributive property to multiply \frac{4}{5} by k+1.

$$4k-4+\frac{4}{5}k+\frac{4}{5}=\frac{1}{4}\left(2k+3\right)$$

Combine 4k and \frac{4}{5}k to get \frac{24}{5}k.

$$\frac{24}{5}k-4+\frac{4}{5}=\frac{1}{4}\left(2k+3\right)$$

Convert -4 to fraction -\frac{20}{5}.

$$\frac{24}{5}k-\frac{20}{5}+\frac{4}{5}=\frac{1}{4}\left(2k+3\right)$$

Since -\frac{20}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{24}{5}k+\frac{-20+4}{5}=\frac{1}{4}\left(2k+3\right)$$

Add -20 and 4 to get -16.

$$\frac{24}{5}k-\frac{16}{5}=\frac{1}{4}\left(2k+3\right)$$

Use the distributive property to multiply \frac{1}{4} by 2k+3.

$$\frac{24}{5}k-\frac{16}{5}=\frac{1}{4}\times 2k+\frac{1}{4}\times 3$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{24}{5}k-\frac{16}{5}=\frac{2}{4}k+\frac{1}{4}\times 3$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{24}{5}k-\frac{16}{5}=\frac{1}{2}k+\frac{1}{4}\times 3$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{24}{5}k-\frac{16}{5}=\frac{1}{2}k+\frac{3}{4}$$

Subtract \frac{1}{2}k from both sides.

$$\frac{24}{5}k-\frac{16}{5}-\frac{1}{2}k=\frac{3}{4}$$

Combine \frac{24}{5}k and -\frac{1}{2}k to get \frac{43}{10}k.

$$\frac{43}{10}k-\frac{16}{5}=\frac{3}{4}$$

Add \frac{16}{5} to both sides.

$$\frac{43}{10}k=\frac{3}{4}+\frac{16}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{16}{5} to fractions with denominator 20.

$$\frac{43}{10}k=\frac{15}{20}+\frac{64}{20}$$

Since \frac{15}{20} and \frac{64}{20} have the same denominator, add them by adding their numerators.

$$\frac{43}{10}k=\frac{15+64}{20}$$

Add 15 and 64 to get 79.

$$\frac{43}{10}k=\frac{79}{20}$$

Multiply both sides by \frac{10}{43}, the reciprocal of \frac{43}{10}.

$$k=\frac{79}{20}\times \frac{10}{43}$$

Multiply \frac{79}{20} times \frac{10}{43} by multiplying numerator times numerator and denominator times denominator.

$$k=\frac{79\times 10}{20\times 43}$$

Do the multiplications in the fraction \frac{79\times 10}{20\times 43}.

$$k=\frac{790}{860}$$

Reduce the fraction \frac{790}{860} to lowest terms by extracting and canceling out 10.

$$k=\frac{79}{86}$$