Solve 2x-4-3x/5/15=7x-x-3/2/5-x+1

$$\frac { 2 x - \frac { 4 - 3 x } { 5 } } { 15 } = \frac { 7 x - \frac { x - 3 } { 2 } } { 5 } - x + 1$$

Solve for x

$$x = -\frac{203}{19} = -10\frac{13}{19} \approx -10.684210526$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 15,5.

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

Use the distributive property to multiply 3 by 7x-\frac{x-3}{2}.

$$2x-\frac{4-3x}{5}=21x+3\left(-\frac{x-3}{2}\right)-15x+15$$

Express 3\left(-\frac{x-3}{2}\right) as a single fraction.

$$2x-\frac{4-3x}{5}=21x+\frac{-3\left(x-3\right)}{2}-15x+15$$

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

$$2x-\frac{4-3x}{5}=21x+\frac{-3x+9}{2}-15x+15$$

Combine 21x and -15x to get 6x.

$$2x-\frac{4-3x}{5}=6x+\frac{-3x+9}{2}+15$$

Divide each term of 4-3x by 5 to get \frac{4}{5}-\frac{3}{5}x.

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

To find the opposite of \frac{4}{5}-\frac{3}{5}x, find the opposite of each term.

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

The opposite of -\frac{3}{5}x is \frac{3}{5}x.

$$2x-\frac{4}{5}+\frac{3}{5}x=6x+\frac{-3x+9}{2}+15$$

Combine 2x and \frac{3}{5}x to get \frac{13}{5}x.

$$\frac{13}{5}x-\frac{4}{5}=6x+\frac{-3x+9}{2}+15$$

Divide each term of -3x+9 by 2 to get -\frac{3}{2}x+\frac{9}{2}.

$$\frac{13}{5}x-\frac{4}{5}=6x-\frac{3}{2}x+\frac{9}{2}+15$$

Combine 6x and -\frac{3}{2}x to get \frac{9}{2}x.

$$\frac{13}{5}x-\frac{4}{5}=\frac{9}{2}x+\frac{9}{2}+15$$

Convert 15 to fraction \frac{30}{2}.

$$\frac{13}{5}x-\frac{4}{5}=\frac{9}{2}x+\frac{9}{2}+\frac{30}{2}$$

Since \frac{9}{2} and \frac{30}{2} have the same denominator, add them by adding their numerators.

$$\frac{13}{5}x-\frac{4}{5}=\frac{9}{2}x+\frac{9+30}{2}$$

Add 9 and 30 to get 39.

$$\frac{13}{5}x-\frac{4}{5}=\frac{9}{2}x+\frac{39}{2}$$

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

$$\frac{13}{5}x-\frac{4}{5}-\frac{9}{2}x=\frac{39}{2}$$

Combine \frac{13}{5}x and -\frac{9}{2}x to get -\frac{19}{10}x.

$$-\frac{19}{10}x-\frac{4}{5}=\frac{39}{2}$$

Add \frac{4}{5} to both sides.

$$-\frac{19}{10}x=\frac{39}{2}+\frac{4}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{39}{2} and \frac{4}{5} to fractions with denominator 10.

$$-\frac{19}{10}x=\frac{195}{10}+\frac{8}{10}$$

Since \frac{195}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$-\frac{19}{10}x=\frac{195+8}{10}$$

Add 195 and 8 to get 203.

$$-\frac{19}{10}x=\frac{203}{10}$$

Multiply both sides by -\frac{10}{19}, the reciprocal of -\frac{19}{10}.

$$x=\frac{203}{10}\left(-\frac{10}{19}\right)$$

Multiply \frac{203}{10} times -\frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{203\left(-10\right)}{10\times 19}$$

Do the multiplications in the fraction \frac{203\left(-10\right)}{10\times 19}.

$$x=\frac{-2030}{190}$$

Reduce the fraction \frac{-2030}{190} to lowest terms by extracting and canceling out 10.

$$x=-\frac{203}{19}$$