Solve 1-x-1/3+1-3x/5=1-2x/3-7-13x/15

$$1 - \frac { x - 1 } { 3 } + \frac { 1 - 3 x } { 5 } = \frac { 1 - 2 x } { 3 } - \frac { 7 - 13 x } { 15 }$$

Solve for x

$$x = \frac{25}{17} = 1\frac{8}{17} \approx 1.470588235$$

Steps for Solving Linear Equation

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

$$15-5\left(x-1\right)+3\left(1-3x\right)=5\left(1-2x\right)-\left(7-13x\right)$$

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

$$15-5x+5+3\left(1-3x\right)=5\left(1-2x\right)-\left(7-13x\right)$$

Add 15 and 5 to get 20.

$$20-5x+3\left(1-3x\right)=5\left(1-2x\right)-\left(7-13x\right)$$

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

$$20-5x+3-9x=5\left(1-2x\right)-\left(7-13x\right)$$

Add 20 and 3 to get 23.

$$23-5x-9x=5\left(1-2x\right)-\left(7-13x\right)$$

Combine -5x and -9x to get -14x.

$$23-14x=5\left(1-2x\right)-\left(7-13x\right)$$

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

$$23-14x=5-10x-\left(7-13x\right)$$

To find the opposite of 7-13x, find the opposite of each term.

$$23-14x=5-10x-7-\left(-13x\right)$$

The opposite of -13x is 13x.

$$23-14x=5-10x-7+13x$$

Subtract 7 from 5 to get -2.

$$23-14x=-2-10x+13x$$

Combine -10x and 13x to get 3x.

$$23-14x=-2+3x$$

Subtract 3x from both sides.

$$23-14x-3x=-2$$

Combine -14x and -3x to get -17x.

$$23-17x=-2$$

Subtract 23 from both sides.

$$-17x=-2-23$$

Subtract 23 from -2 to get -25.

$$-17x=-25$$

Divide both sides by -17.

$$x=\frac{-25}{-17}$$

Fraction \frac{-25}{-17} can be simplified to \frac{25}{17} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{17}$$