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

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

Solve for k

$$k=1$$

Steps for Solving Linear Equation

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

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

Cancel out 2 and 2.

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

Multiply \frac{3}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Divide 4 by 2 to get 2.

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

Subtract 4 from 2 to get -2.

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

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

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

Multiply \frac{5}{4} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

Subtract \frac{5}{4}k from both sides.

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

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

$$\frac{7}{4}k-2=-\frac{1}{4}$$

Add 2 to both sides.

$$\frac{7}{4}k=-\frac{1}{4}+2$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{7}{4}k=-\frac{1}{4}+\frac{8}{4}$$

Since -\frac{1}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{7}{4}k=\frac{-1+8}{4}$$

Add -1 and 8 to get 7.

$$\frac{7}{4}k=\frac{7}{4}$$

Multiply both sides by \frac{4}{7}, the reciprocal of \frac{7}{4}.

$$k=\frac{7}{4}\times \frac{4}{7}$$

Cancel out \frac{7}{4} and its reciprocal \frac{4}{7}.

$$k=1$$