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

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

Solve for x

$$x = -\frac{46}{17} = -2\frac{12}{17} \approx -2.705882353$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$6\left(2x+1\right)-5\left(4-x\right)=-60$$

Use the distributive property to multiply 6 by 2x+1.

$$12x+6-5\left(4-x\right)=-60$$

Use the distributive property to multiply -5 by 4-x.

$$12x+6-20+5x=-60$$

Subtract 20 from 6 to get -14.

$$12x-14+5x=-60$$

Combine 12x and 5x to get 17x.

$$17x-14=-60$$

Add 14 to both sides.

$$17x=-60+14$$

Add -60 and 14 to get -46.

$$17x=-46$$

Divide both sides by 17.

$$x=\frac{-46}{17}$$

Fraction \frac{-46}{17} can be rewritten as -\frac{46}{17} by extracting the negative sign.

$$x=-\frac{46}{17}$$