Solve 2x/3+4/5-3/2left(8x/15+frac{4}{9}right)=frac{7}{4}-frac{4}{3}left(frac{6}{5}-frac{9x}{2}right)

$$\frac{ 2x }{ 3 } + \frac{ 4 }{ 5 } - \frac{ 3 }{ 2 } \left( \frac{ 8x }{ 15 } + \frac{ 4 }{ 9 } \right) = \frac{ 7 }{ 4 } - \frac{ 4 }{ 3 } \left( \frac{ 6 }{ 5 } - \frac{ 9x }{ 2 } \right)$$

Solve for x

$$x=-\frac{1}{368}\approx -0.002717391$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 180, the least common multiple of 3,5,2,15,9,4.

$$180\left(\frac{2x}{3}+\frac{4}{5}\right)-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{2x}{3} times \frac{5}{5}. Multiply \frac{4}{5} times \frac{3}{3}.

$$180\left(\frac{5\times 2x}{15}+\frac{4\times 3}{15}\right)-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Since \frac{5\times 2x}{15} and \frac{4\times 3}{15} have the same denominator, add them by adding their numerators.

$$180\times \frac{5\times 2x+4\times 3}{15}-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Do the multiplications in 5\times 2x+4\times 3.

$$180\times \frac{10x+12}{15}-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Cancel out 15, the greatest common factor in 180 and 15.

$$12\left(10x+12\right)-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Use the distributive property to multiply 12 by 10x+12.

$$120x+144-270\left(\frac{8x}{15}+\frac{4}{9}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 9 is 45. Multiply \frac{8x}{15} times \frac{3}{3}. Multiply \frac{4}{9} times \frac{5}{5}.

$$120x+144-270\left(\frac{3\times 8x}{45}+\frac{4\times 5}{45}\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Since \frac{3\times 8x}{45} and \frac{4\times 5}{45} have the same denominator, add them by adding their numerators.

$$120x+144-270\times \frac{3\times 8x+4\times 5}{45}=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Do the multiplications in 3\times 8x+4\times 5.

$$120x+144-270\times \frac{24x+20}{45}=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Cancel out 45, the greatest common factor in 270 and 45.

$$120x+144-6\left(24x+20\right)=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Use the distributive property to multiply -6 by 24x+20.

$$120x+144-144x-120=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Combine 120x and -144x to get -24x.

$$-24x+144-120=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

Subtract 120 from 144 to get 24.

$$-24x+24=315-240\left(\frac{6}{5}-\frac{9x}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{6}{5} times \frac{2}{2}. Multiply \frac{9x}{2} times \frac{5}{5}.

$$-24x+24=315-240\left(\frac{6\times 2}{10}-\frac{5\times 9x}{10}\right)$$

Since \frac{6\times 2}{10} and \frac{5\times 9x}{10} have the same denominator, subtract them by subtracting their numerators.

$$-24x+24=315-240\times \frac{6\times 2-5\times 9x}{10}$$

Do the multiplications in 6\times 2-5\times 9x.

$$-24x+24=315-240\times \frac{12-45x}{10}$$

Cancel out 10, the greatest common factor in 240 and 10.

$$-24x+24=315-24\left(12-45x\right)$$

Use the distributive property to multiply -24 by 12-45x.

$$-24x+24=315-288+1080x$$

Subtract 288 from 315 to get 27.

$$-24x+24=27+1080x$$

Subtract 1080x from both sides.

$$-24x+24-1080x=27$$

Combine -24x and -1080x to get -1104x.

$$-1104x+24=27$$

Subtract 24 from both sides.

$$-1104x=27-24$$

Subtract 24 from 27 to get 3.

$$-1104x=3$$

Divide both sides by -1104.

$$x=\frac{3}{-1104}$$

Reduce the fraction \frac{3}{-1104} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{368}$$