Solve x-1/3*4*5-5-2x/2*4*5=-3x+4/3*5*6

$$\frac { x - 1 } { 3 \times 4 \times 5 } - \frac { 5 - 2 x } { 2 \times 4 \times 5 } = - \frac { 3 x + 4 } { 3 \times 5 \times 6 }$$

Solve for x

$$x=\frac{35}{36}\approx 0.972222222$$

Steps for Solving Linear Equation

Multiply 3 and 4 to get 12.

$$\frac{x-1}{12\times 5}-\frac{5-2x}{2\times 4\times 5}=-\frac{3x+4}{3\times 5\times 6}$$

Multiply 12 and 5 to get 60.

$$\frac{x-1}{60}-\frac{5-2x}{2\times 4\times 5}=-\frac{3x+4}{3\times 5\times 6}$$

Multiply 2 and 4 to get 8.

$$\frac{x-1}{60}-\frac{5-2x}{8\times 5}=-\frac{3x+4}{3\times 5\times 6}$$

Multiply 8 and 5 to get 40.

$$\frac{x-1}{60}-\frac{5-2x}{40}=-\frac{3x+4}{3\times 5\times 6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 60 and 40 is 120. Multiply \frac{x-1}{60} times \frac{2}{2}. Multiply \frac{5-2x}{40} times \frac{3}{3}.

$$\frac{2\left(x-1\right)}{120}-\frac{3\left(5-2x\right)}{120}=-\frac{3x+4}{3\times 5\times 6}$$

Since \frac{2\left(x-1\right)}{120} and \frac{3\left(5-2x\right)}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(x-1\right)-3\left(5-2x\right)}{120}=-\frac{3x+4}{3\times 5\times 6}$$

Do the multiplications in 2\left(x-1\right)-3\left(5-2x\right).

$$\frac{2x-2-15+6x}{120}=-\frac{3x+4}{3\times 5\times 6}$$

Combine like terms in 2x-2-15+6x.

$$\frac{8x-17}{120}=-\frac{3x+4}{3\times 5\times 6}$$

Multiply 3 and 5 to get 15.

$$\frac{8x-17}{120}=-\frac{3x+4}{15\times 6}$$

Multiply 15 and 6 to get 90.

$$\frac{8x-17}{120}=-\frac{3x+4}{90}$$

Divide each term of 8x-17 by 120 to get \frac{1}{15}x-\frac{17}{120}.

$$\frac{1}{15}x-\frac{17}{120}=-\frac{3x+4}{90}$$

Divide each term of 3x+4 by 90 to get \frac{1}{30}x+\frac{2}{45}.

$$\frac{1}{15}x-\frac{17}{120}=-\left(\frac{1}{30}x+\frac{2}{45}\right)$$

To find the opposite of \frac{1}{30}x+\frac{2}{45}, find the opposite of each term.

$$\frac{1}{15}x-\frac{17}{120}=-\frac{1}{30}x-\frac{2}{45}$$

Add \frac{1}{30}x to both sides.

$$\frac{1}{15}x-\frac{17}{120}+\frac{1}{30}x=-\frac{2}{45}$$

Combine \frac{1}{15}x and \frac{1}{30}x to get \frac{1}{10}x.

$$\frac{1}{10}x-\frac{17}{120}=-\frac{2}{45}$$

Add \frac{17}{120} to both sides.

$$\frac{1}{10}x=-\frac{2}{45}+\frac{17}{120}$$

Least common multiple of 45 and 120 is 360. Convert -\frac{2}{45} and \frac{17}{120} to fractions with denominator 360.

$$\frac{1}{10}x=-\frac{16}{360}+\frac{51}{360}$$

Since -\frac{16}{360} and \frac{51}{360} have the same denominator, add them by adding their numerators.

$$\frac{1}{10}x=\frac{-16+51}{360}$$

Add -16 and 51 to get 35.

$$\frac{1}{10}x=\frac{35}{360}$$

Reduce the fraction \frac{35}{360} to lowest terms by extracting and canceling out 5.

$$\frac{1}{10}x=\frac{7}{72}$$

Multiply both sides by 10, the reciprocal of \frac{1}{10}.

$$x=\frac{7}{72}\times 10$$

Express \frac{7}{72}\times 10 as a single fraction.

$$x=\frac{7\times 10}{72}$$

Multiply 7 and 10 to get 70.

$$x=\frac{70}{72}$$

Reduce the fraction \frac{70}{72} to lowest terms by extracting and canceling out 2.

$$x=\frac{35}{36}$$