Solve 3x-x+1/2=x/3-7/6

$$3 x - \frac { x + 1 } { 2 } = \frac { x } { 3 } - \frac { 7 } { 6 }$$

Solve for x

$$x=-\frac{4}{13}\approx -0.307692308$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$18x-3\left(x+1\right)=2x-7$$

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

$$18x-3x-3=2x-7$$

Combine 18x and -3x to get 15x.

$$15x-3=2x-7$$

Subtract 2x from both sides.

$$15x-3-2x=-7$$

Combine 15x and -2x to get 13x.

$$13x-3=-7$$

Add 3 to both sides.

$$13x=-7+3$$

Add -7 and 3 to get -4.

$$13x=-4$$

Divide both sides by 13.

$$x=\frac{-4}{13}$$

Fraction \frac{-4}{13} can be rewritten as -\frac{4}{13} by extracting the negative sign.

$$x=-\frac{4}{13}$$