Solve 2/3(5x-7)=4/5

$$\frac { 2 } { 3 } ( 5 x - 7 ) = \frac { 4 } { 5 }$$

Solve for x

$$x = \frac{41}{25} = 1\frac{16}{25} = 1.64$$

Steps for Solving Linear Equation

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.

$$5x-7=\frac{4}{5}\times \frac{3}{2}$$

Multiply \frac{4}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$5x-7=\frac{4\times 3}{5\times 2}$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 2}.

$$5x-7=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$5x-7=\frac{6}{5}$$

Add 7 to both sides.

$$5x=\frac{6}{5}+7$$

Convert 7 to fraction \frac{35}{5}.

$$5x=\frac{6}{5}+\frac{35}{5}$$

Since \frac{6}{5} and \frac{35}{5} have the same denominator, add them by adding their numerators.

$$5x=\frac{6+35}{5}$$

Add 6 and 35 to get 41.

$$5x=\frac{41}{5}$$

Divide both sides by 5.

$$x=\frac{\frac{41}{5}}{5}$$

Express \frac{\frac{41}{5}}{5} as a single fraction.

$$x=\frac{41}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$x=\frac{41}{25}$$