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

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

Solve for x

$$x = -\frac{10}{3} = -3\frac{1}{3} \approx -3.333333333$$

Steps for Solving Linear Equation

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

$$2\left(x-6\right)-3\left(x-4\right)=2\left(x+5\right)$$

Use the distributive property to multiply 2 by x-6.

$$2x-12-3\left(x-4\right)=2\left(x+5\right)$$

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

$$2x-12-3x+12=2\left(x+5\right)$$

Combine 2x and -3x to get -x.

$$-x-12+12=2\left(x+5\right)$$

Add -12 and 12 to get 0.

$$-x=2\left(x+5\right)$$

Use the distributive property to multiply 2 by x+5.

$$-x=2x+10$$

Subtract 2x from both sides.

$$-x-2x=10$$

Combine -x and -2x to get -3x.

$$-3x=10$$

Divide both sides by -3.

$$x=\frac{10}{-3}$$

Fraction \frac{10}{-3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$x=-\frac{10}{3}$$