Solve -943/75+10/3a=4/5(7/4a+frac{6}{5})

$$- \frac { 943 } { 75 } + \frac { 10 } { 3 } a = \frac { 4 } { 5 } ( \frac { 7 } { 4 } a + \frac { 6 } { 5 } )$$

Solve for a

$$a=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{5} by \frac{7}{4}a+\frac{6}{5}.

$$-\frac{943}{75}+\frac{10}{3}a=\frac{4}{5}\times \frac{7}{4}a+\frac{4}{5}\times \frac{6}{5}$$

Multiply \frac{4}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{943}{75}+\frac{10}{3}a=\frac{4\times 7}{5\times 4}a+\frac{4}{5}\times \frac{6}{5}$$

Cancel out 4 in both numerator and denominator.

$$-\frac{943}{75}+\frac{10}{3}a=\frac{7}{5}a+\frac{4}{5}\times \frac{6}{5}$$

Multiply \frac{4}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{943}{75}+\frac{10}{3}a=\frac{7}{5}a+\frac{4\times 6}{5\times 5}$$

Do the multiplications in the fraction \frac{4\times 6}{5\times 5}.

$$-\frac{943}{75}+\frac{10}{3}a=\frac{7}{5}a+\frac{24}{25}$$

Subtract \frac{7}{5}a from both sides.

$$-\frac{943}{75}+\frac{10}{3}a-\frac{7}{5}a=\frac{24}{25}$$

Combine \frac{10}{3}a and -\frac{7}{5}a to get \frac{29}{15}a.

$$-\frac{943}{75}+\frac{29}{15}a=\frac{24}{25}$$

Add \frac{943}{75} to both sides.

$$\frac{29}{15}a=\frac{24}{25}+\frac{943}{75}$$

Least common multiple of 25 and 75 is 75. Convert \frac{24}{25} and \frac{943}{75} to fractions with denominator 75.

$$\frac{29}{15}a=\frac{72}{75}+\frac{943}{75}$$

Since \frac{72}{75} and \frac{943}{75} have the same denominator, add them by adding their numerators.

$$\frac{29}{15}a=\frac{72+943}{75}$$

Add 72 and 943 to get 1015.

$$\frac{29}{15}a=\frac{1015}{75}$$

Reduce the fraction \frac{1015}{75} to lowest terms by extracting and canceling out 5.

$$\frac{29}{15}a=\frac{203}{15}$$

Multiply both sides by \frac{15}{29}, the reciprocal of \frac{29}{15}.

$$a=\frac{203}{15}\times \frac{15}{29}$$

Multiply \frac{203}{15} times \frac{15}{29} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{203\times 15}{15\times 29}$$

Cancel out 15 in both numerator and denominator.

$$a=\frac{203}{29}$$

Divide 203 by 29 to get 7.

$$a=7$$