Solve 7/2-(3/10-x)=sqrt{9/25}+3/4*(2x+frac{8}{5})

$$\frac { 7 } { 2 } - ( \frac { 3 } { 10 } - x ) = \sqrt { \frac { 9 } { 25 } } + \frac { 3 } { 4 } \cdot ( 2 x + \frac { 8 } { 5 } )$$

Solve for x

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps for Solving Linear Equation

To find the opposite of \frac{3}{10}-x, find the opposite of each term.

$$\frac{7}{2}-\frac{3}{10}-\left(-x\right)=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

The opposite of -x is x.

$$\frac{7}{2}-\frac{3}{10}+x=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Least common multiple of 2 and 10 is 10. Convert \frac{7}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{35}{10}-\frac{3}{10}+x=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Since \frac{35}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-3}{10}+x=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Subtract 3 from 35 to get 32.

$$\frac{32}{10}+x=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{16}{5}+x=\sqrt{\frac{9}{25}}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{4}\left(2x+\frac{8}{5}\right)$$

Use the distributive property to multiply \frac{3}{4} by 2x+\frac{8}{5}.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{4}\times 2x+\frac{3}{4}\times \frac{8}{5}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3\times 2}{4}x+\frac{3}{4}\times \frac{8}{5}$$

Multiply 3 and 2 to get 6.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{6}{4}x+\frac{3}{4}\times \frac{8}{5}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{2}x+\frac{3}{4}\times \frac{8}{5}$$

Multiply \frac{3}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{2}x+\frac{3\times 8}{4\times 5}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 5}.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{2}x+\frac{24}{20}$$

Reduce the fraction \frac{24}{20} to lowest terms by extracting and canceling out 4.

$$\frac{16}{5}+x=\frac{3}{5}+\frac{3}{2}x+\frac{6}{5}$$

Since \frac{3}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$\frac{16}{5}+x=\frac{3+6}{5}+\frac{3}{2}x$$

Add 3 and 6 to get 9.

$$\frac{16}{5}+x=\frac{9}{5}+\frac{3}{2}x$$

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

$$\frac{16}{5}+x-\frac{3}{2}x=\frac{9}{5}$$

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

$$\frac{16}{5}-\frac{1}{2}x=\frac{9}{5}$$

Subtract \frac{16}{5} from both sides.

$$-\frac{1}{2}x=\frac{9}{5}-\frac{16}{5}$$

Since \frac{9}{5} and \frac{16}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}x=\frac{9-16}{5}$$

Subtract 16 from 9 to get -7.

$$-\frac{1}{2}x=-\frac{7}{5}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-\frac{7}{5}\left(-2\right)$$

Express -\frac{7}{5}\left(-2\right) as a single fraction.

$$x=\frac{-7\left(-2\right)}{5}$$

Multiply -7 and -2 to get 14.

$$x=\frac{14}{5}$$