Solve 3-2x-1/3=4-3x/5-x

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

Solve for x

$$x = -\frac{19}{7} = -2\frac{5}{7} \approx -2.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$45-5\left(2x-1\right)=3\left(4-3x\right)-15x$$

Use the distributive property to multiply -5 by 2x-1.

$$45-10x+5=3\left(4-3x\right)-15x$$

Add 45 and 5 to get 50.

$$50-10x=3\left(4-3x\right)-15x$$

Use the distributive property to multiply 3 by 4-3x.

$$50-10x=12-9x-15x$$

Combine -9x and -15x to get -24x.

$$50-10x=12-24x$$

Add 24x to both sides.

$$50-10x+24x=12$$

Combine -10x and 24x to get 14x.

$$50+14x=12$$

Subtract 50 from both sides.

$$14x=12-50$$

Subtract 50 from 12 to get -38.

$$14x=-38$$

Divide both sides by 14.

$$x=\frac{-38}{14}$$

Reduce the fraction \frac{-38}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{19}{7}$$