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

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

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 4,2,3,5.

$$60\left(\frac{3x-1}{\frac{3}{5}}-\frac{3}{4}\left(\frac{2x-5}{2}+x\right)\right)-8\left(1-3x\right)=180$$

Use the distributive property to multiply -8 by 1-3x.

$$60\left(\frac{3x-1}{\frac{3}{5}}-\frac{3}{4}\left(\frac{2x-5}{2}+x\right)\right)-8+24x=180$$

Divide each term of 3x-1 by \frac{3}{5} to get \frac{3x}{\frac{3}{5}}+\frac{-1}{\frac{3}{5}}.

$$60\left(\frac{3x}{\frac{3}{5}}+\frac{-1}{\frac{3}{5}}-\frac{3}{4}\left(\frac{2x-5}{2}+x\right)\right)-8+24x=180$$

Divide 3x by \frac{3}{5} to get 5x.

$$60\left(5x+\frac{-1}{\frac{3}{5}}-\frac{3}{4}\left(\frac{2x-5}{2}+x\right)\right)-8+24x=180$$

Divide -1 by \frac{3}{5} by multiplying -1 by the reciprocal of \frac{3}{5}.

$$60\left(5x-\frac{5}{3}-\frac{3}{4}\left(\frac{2x-5}{2}+x\right)\right)-8+24x=180$$

Divide each term of 2x-5 by 2 to get x-\frac{5}{2}.

$$60\left(5x-\frac{5}{3}-\frac{3}{4}\left(x-\frac{5}{2}+x\right)\right)-8+24x=180$$

Combine x and x to get 2x.

$$60\left(5x-\frac{5}{3}-\frac{3}{4}\left(2x-\frac{5}{2}\right)\right)-8+24x=180$$

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

$$60\left(5x-\frac{5}{3}-\frac{3}{4}\times 2x-\frac{3}{4}\left(-\frac{5}{2}\right)\right)-8+24x=180$$

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

$$60\left(5x-\frac{5}{3}+\frac{-3\times 2}{4}x-\frac{3}{4}\left(-\frac{5}{2}\right)\right)-8+24x=180$$

Multiply -3 and 2 to get -6.

$$60\left(5x-\frac{5}{3}+\frac{-6}{4}x-\frac{3}{4}\left(-\frac{5}{2}\right)\right)-8+24x=180$$

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

$$60\left(5x-\frac{5}{3}-\frac{3}{2}x-\frac{3}{4}\left(-\frac{5}{2}\right)\right)-8+24x=180$$

Multiply -\frac{3}{4} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$60\left(5x-\frac{5}{3}-\frac{3}{2}x+\frac{-3\left(-5\right)}{4\times 2}\right)-8+24x=180$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{4\times 2}.

$$60\left(5x-\frac{5}{3}-\frac{3}{2}x+\frac{15}{8}\right)-8+24x=180$$

Combine 5x and -\frac{3}{2}x to get \frac{7}{2}x.

$$60\left(\frac{7}{2}x-\frac{5}{3}+\frac{15}{8}\right)-8+24x=180$$

Least common multiple of 3 and 8 is 24. Convert -\frac{5}{3} and \frac{15}{8} to fractions with denominator 24.

$$60\left(\frac{7}{2}x-\frac{40}{24}+\frac{45}{24}\right)-8+24x=180$$

Since -\frac{40}{24} and \frac{45}{24} have the same denominator, add them by adding their numerators.

$$60\left(\frac{7}{2}x+\frac{-40+45}{24}\right)-8+24x=180$$

Add -40 and 45 to get 5.

$$60\left(\frac{7}{2}x+\frac{5}{24}\right)-8+24x=180$$

Use the distributive property to multiply 60 by \frac{7}{2}x+\frac{5}{24}.

$$60\times \frac{7}{2}x+60\times \frac{5}{24}-8+24x=180$$

Express 60\times \frac{7}{2} as a single fraction.

$$\frac{60\times 7}{2}x+60\times \frac{5}{24}-8+24x=180$$

Multiply 60 and 7 to get 420.

$$\frac{420}{2}x+60\times \frac{5}{24}-8+24x=180$$

Divide 420 by 2 to get 210.

$$210x+60\times \frac{5}{24}-8+24x=180$$

Express 60\times \frac{5}{24} as a single fraction.

$$210x+\frac{60\times 5}{24}-8+24x=180$$

Multiply 60 and 5 to get 300.

$$210x+\frac{300}{24}-8+24x=180$$

Reduce the fraction \frac{300}{24} to lowest terms by extracting and canceling out 12.

$$210x+\frac{25}{2}-8+24x=180$$

Convert 8 to fraction \frac{16}{2}.

$$210x+\frac{25}{2}-\frac{16}{2}+24x=180$$

Since \frac{25}{2} and \frac{16}{2} have the same denominator, subtract them by subtracting their numerators.

$$210x+\frac{25-16}{2}+24x=180$$

Subtract 16 from 25 to get 9.

$$210x+\frac{9}{2}+24x=180$$

Combine 210x and 24x to get 234x.

$$234x+\frac{9}{2}=180$$

Subtract \frac{9}{2} from both sides.

$$234x=180-\frac{9}{2}$$

Convert 180 to fraction \frac{360}{2}.

$$234x=\frac{360}{2}-\frac{9}{2}$$

Since \frac{360}{2} and \frac{9}{2} have the same denominator, subtract them by subtracting their numerators.

$$234x=\frac{360-9}{2}$$

Subtract 9 from 360 to get 351.

$$234x=\frac{351}{2}$$

Divide both sides by 234.

$$x=\frac{\frac{351}{2}}{234}$$

Express \frac{\frac{351}{2}}{234} as a single fraction.

$$x=\frac{351}{2\times 234}$$

Multiply 2 and 234 to get 468.

$$x=\frac{351}{468}$$

Reduce the fraction \frac{351}{468} to lowest terms by extracting and canceling out 117.

$$x=\frac{3}{4}$$