Solve 2x-5/6+x+2/4=5-2x/3-6-7x/5-x

$$\frac { 2 x - 5 } { 6 } + \frac { x + 2 } { 4 } = \frac { 5 - 2 x } { 3 } - \frac { 6 - 7 x } { 5 } - x$$

Solve for x

$$x=\frac{16}{17}\approx 0.941176471$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 6,4,3,5.

$$10\left(2x-5\right)+15\left(x+2\right)=20\left(5-2x\right)-12\left(6-7x\right)-60x$$

Use the distributive property to multiply 10 by 2x-5.

$$20x-50+15\left(x+2\right)=20\left(5-2x\right)-12\left(6-7x\right)-60x$$

Use the distributive property to multiply 15 by x+2.

$$20x-50+15x+30=20\left(5-2x\right)-12\left(6-7x\right)-60x$$

Combine 20x and 15x to get 35x.

$$35x-50+30=20\left(5-2x\right)-12\left(6-7x\right)-60x$$

Add -50 and 30 to get -20.

$$35x-20=20\left(5-2x\right)-12\left(6-7x\right)-60x$$

Use the distributive property to multiply 20 by 5-2x.

$$35x-20=100-40x-12\left(6-7x\right)-60x$$

Use the distributive property to multiply -12 by 6-7x.

$$35x-20=100-40x-72+84x-60x$$

Subtract 72 from 100 to get 28.

$$35x-20=28-40x+84x-60x$$

Combine -40x and 84x to get 44x.

$$35x-20=28+44x-60x$$

Combine 44x and -60x to get -16x.

$$35x-20=28-16x$$

Add 16x to both sides.

$$35x-20+16x=28$$

Combine 35x and 16x to get 51x.

$$51x-20=28$$

Add 20 to both sides.

$$51x=28+20$$

Add 28 and 20 to get 48.

$$51x=48$$

Divide both sides by 51.

$$x=\frac{48}{51}$$

Reduce the fraction \frac{48}{51} to lowest terms by extracting and canceling out 3.

$$x=\frac{16}{17}$$