Solve 5/3+9/2*(1/4-25x)+3x-(4/5+6)=7x+9x-frac{2}{5}

$$\frac { 5 } { 3 } + \frac { 9 } { 2 } \cdot ( \frac { 1 } { 4 } - 25 x ) + 3 x - ( \frac { 4 } { 5 } + 6 ) = 7 x + 9 x - \frac { 2 } { 5 }$$

Solve for x

$$x=-\frac{433}{15060}\approx -0.02875166$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{9}{2} by \frac{1}{4}-25x.

$$\frac{5}{3}+\frac{9}{2}\times \frac{1}{4}+\frac{9}{2}\left(-25\right)x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Multiply \frac{9}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{3}+\frac{9\times 1}{2\times 4}+\frac{9}{2}\left(-25\right)x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Do the multiplications in the fraction \frac{9\times 1}{2\times 4}.

$$\frac{5}{3}+\frac{9}{8}+\frac{9}{2}\left(-25\right)x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Express \frac{9}{2}\left(-25\right) as a single fraction.

$$\frac{5}{3}+\frac{9}{8}+\frac{9\left(-25\right)}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Multiply 9 and -25 to get -225.

$$\frac{5}{3}+\frac{9}{8}+\frac{-225}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Fraction \frac{-225}{2} can be rewritten as -\frac{225}{2} by extracting the negative sign.

$$\frac{5}{3}+\frac{9}{8}-\frac{225}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Least common multiple of 3 and 8 is 24. Convert \frac{5}{3} and \frac{9}{8} to fractions with denominator 24.

$$\frac{40}{24}+\frac{27}{24}-\frac{225}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Since \frac{40}{24} and \frac{27}{24} have the same denominator, add them by adding their numerators.

$$\frac{40+27}{24}-\frac{225}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Add 40 and 27 to get 67.

$$\frac{67}{24}-\frac{225}{2}x+3x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Combine -\frac{225}{2}x and 3x to get -\frac{219}{2}x.

$$\frac{67}{24}-\frac{219}{2}x-\left(\frac{4}{5}+6\right)=7x+9x-\frac{2}{5}$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{67}{24}-\frac{219}{2}x-\left(\frac{4}{5}+\frac{30}{5}\right)=7x+9x-\frac{2}{5}$$

Since \frac{4}{5} and \frac{30}{5} have the same denominator, add them by adding their numerators.

$$\frac{67}{24}-\frac{219}{2}x-\frac{4+30}{5}=7x+9x-\frac{2}{5}$$

Add 4 and 30 to get 34.

$$\frac{67}{24}-\frac{219}{2}x-\frac{34}{5}=7x+9x-\frac{2}{5}$$

Least common multiple of 24 and 5 is 120. Convert \frac{67}{24} and \frac{34}{5} to fractions with denominator 120.

$$\frac{335}{120}-\frac{219}{2}x-\frac{816}{120}=7x+9x-\frac{2}{5}$$

Since \frac{335}{120} and \frac{816}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{335-816}{120}-\frac{219}{2}x=7x+9x-\frac{2}{5}$$

Subtract 816 from 335 to get -481.

$$-\frac{481}{120}-\frac{219}{2}x=7x+9x-\frac{2}{5}$$

Combine 7x and 9x to get 16x.

$$-\frac{481}{120}-\frac{219}{2}x=16x-\frac{2}{5}$$

Subtract 16x from both sides.

$$-\frac{481}{120}-\frac{219}{2}x-16x=-\frac{2}{5}$$

Combine -\frac{219}{2}x and -16x to get -\frac{251}{2}x.

$$-\frac{481}{120}-\frac{251}{2}x=-\frac{2}{5}$$

Add \frac{481}{120} to both sides.

$$-\frac{251}{2}x=-\frac{2}{5}+\frac{481}{120}$$

Least common multiple of 5 and 120 is 120. Convert -\frac{2}{5} and \frac{481}{120} to fractions with denominator 120.

$$-\frac{251}{2}x=-\frac{48}{120}+\frac{481}{120}$$

Since -\frac{48}{120} and \frac{481}{120} have the same denominator, add them by adding their numerators.

$$-\frac{251}{2}x=\frac{-48+481}{120}$$

Add -48 and 481 to get 433.

$$-\frac{251}{2}x=\frac{433}{120}$$

Multiply both sides by -\frac{2}{251}, the reciprocal of -\frac{251}{2}.

$$x=\frac{433}{120}\left(-\frac{2}{251}\right)$$

Multiply \frac{433}{120} times -\frac{2}{251} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{433\left(-2\right)}{120\times 251}$$

Do the multiplications in the fraction \frac{433\left(-2\right)}{120\times 251}.

$$x=\frac{-866}{30120}$$

Reduce the fraction \frac{-866}{30120} to lowest terms by extracting and canceling out 2.

$$x=-\frac{433}{15060}$$