Solve x-7/2-2/3=2/3*(3/4x-frac{2}{5})

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

Solve for x

$$x = \frac{39}{5} = 7\frac{4}{5} = 7.8$$

Steps for Solving Linear Equation

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{2}{3} to fractions with denominator 6.

$$x-\frac{21}{6}-\frac{4}{6}=\frac{2}{3}\left(\frac{3}{4}x-\frac{2}{5}\right)$$

Since -\frac{21}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{-21-4}{6}=\frac{2}{3}\left(\frac{3}{4}x-\frac{2}{5}\right)$$

Subtract 4 from -21 to get -25.

$$x-\frac{25}{6}=\frac{2}{3}\left(\frac{3}{4}x-\frac{2}{5}\right)$$

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

$$x-\frac{25}{6}=\frac{2}{3}\times \frac{3}{4}x+\frac{2}{3}\left(-\frac{2}{5}\right)$$

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

$$x-\frac{25}{6}=\frac{2\times 3}{3\times 4}x+\frac{2}{3}\left(-\frac{2}{5}\right)$$

Cancel out 3 in both numerator and denominator.

$$x-\frac{25}{6}=\frac{2}{4}x+\frac{2}{3}\left(-\frac{2}{5}\right)$$

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

$$x-\frac{25}{6}=\frac{1}{2}x+\frac{2}{3}\left(-\frac{2}{5}\right)$$

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

$$x-\frac{25}{6}=\frac{1}{2}x+\frac{2\left(-2\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{2\left(-2\right)}{3\times 5}.

$$x-\frac{25}{6}=\frac{1}{2}x+\frac{-4}{15}$$

Fraction \frac{-4}{15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

$$x-\frac{25}{6}=\frac{1}{2}x-\frac{4}{15}$$

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

$$x-\frac{25}{6}-\frac{1}{2}x=-\frac{4}{15}$$

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

$$\frac{1}{2}x-\frac{25}{6}=-\frac{4}{15}$$

Add \frac{25}{6} to both sides.

$$\frac{1}{2}x=-\frac{4}{15}+\frac{25}{6}$$

Least common multiple of 15 and 6 is 30. Convert -\frac{4}{15} and \frac{25}{6} to fractions with denominator 30.

$$\frac{1}{2}x=-\frac{8}{30}+\frac{125}{30}$$

Since -\frac{8}{30} and \frac{125}{30} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x=\frac{-8+125}{30}$$

Add -8 and 125 to get 117.

$$\frac{1}{2}x=\frac{117}{30}$$

Reduce the fraction \frac{117}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}x=\frac{39}{10}$$

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

$$x=\frac{39}{10}\times 2$$

Express \frac{39}{10}\times 2 as a single fraction.

$$x=\frac{39\times 2}{10}$$

Multiply 39 and 2 to get 78.

$$x=\frac{78}{10}$$

Reduce the fraction \frac{78}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{39}{5}$$