Solve 1/4(2x-3)-3/5x=9/4(-5x+3)-1/2

$$\frac { 1 } { 4 } ( 2 x - 3 ) - \frac { 3 } { 5 } x = \frac { 9 } { 4 } ( - 5 x + 3 ) - \frac { 1 } { 2 }$$

Solve for x

$$x=\frac{140}{223}\approx 0.627802691$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by 2x-3.

$$\frac{1}{4}\times 2x+\frac{1}{4}\left(-3\right)-\frac{3}{5}x=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{2}{4}x+\frac{1}{4}\left(-3\right)-\frac{3}{5}x=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

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

$$\frac{1}{2}x+\frac{1}{4}\left(-3\right)-\frac{3}{5}x=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{1}{2}x+\frac{-3}{4}-\frac{3}{5}x=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{2}x-\frac{3}{4}-\frac{3}{5}x=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

Combine \frac{1}{2}x and -\frac{3}{5}x to get -\frac{1}{10}x.

$$-\frac{1}{10}x-\frac{3}{4}=\frac{9}{4}\left(-5x+3\right)-\frac{1}{2}$$

Use the distributive property to multiply \frac{9}{4} by -5x+3.

$$-\frac{1}{10}x-\frac{3}{4}=\frac{9}{4}\left(-5\right)x+\frac{9}{4}\times 3-\frac{1}{2}$$

Express \frac{9}{4}\left(-5\right) as a single fraction.

$$-\frac{1}{10}x-\frac{3}{4}=\frac{9\left(-5\right)}{4}x+\frac{9}{4}\times 3-\frac{1}{2}$$

Multiply 9 and -5 to get -45.

$$-\frac{1}{10}x-\frac{3}{4}=\frac{-45}{4}x+\frac{9}{4}\times 3-\frac{1}{2}$$

Fraction \frac{-45}{4} can be rewritten as -\frac{45}{4} by extracting the negative sign.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{9}{4}\times 3-\frac{1}{2}$$

Express \frac{9}{4}\times 3 as a single fraction.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{9\times 3}{4}-\frac{1}{2}$$

Multiply 9 and 3 to get 27.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{27}{4}-\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{27}{4} and \frac{1}{2} to fractions with denominator 4.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{27}{4}-\frac{2}{4}$$

Since \frac{27}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{27-2}{4}$$

Subtract 2 from 27 to get 25.

$$-\frac{1}{10}x-\frac{3}{4}=-\frac{45}{4}x+\frac{25}{4}$$

Add \frac{45}{4}x to both sides.

$$-\frac{1}{10}x-\frac{3}{4}+\frac{45}{4}x=\frac{25}{4}$$

Combine -\frac{1}{10}x and \frac{45}{4}x to get \frac{223}{20}x.

$$\frac{223}{20}x-\frac{3}{4}=\frac{25}{4}$$

Add \frac{3}{4} to both sides.

$$\frac{223}{20}x=\frac{25}{4}+\frac{3}{4}$$

Since \frac{25}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{223}{20}x=\frac{25+3}{4}$$

Add 25 and 3 to get 28.

$$\frac{223}{20}x=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$\frac{223}{20}x=7$$

Multiply both sides by \frac{20}{223}, the reciprocal of \frac{223}{20}.

$$x=7\times \frac{20}{223}$$

Express 7\times \frac{20}{223} as a single fraction.

$$x=\frac{7\times 20}{223}$$

Multiply 7 and 20 to get 140.

$$x=\frac{140}{223}$$