Solve x-3/2-x+3/5=-10/3

$$\frac { x - 3 } { 2 } - \frac { x + 3 } { 5 } = - \frac { 10 } { 3 }$$

Solve for x

$$x = -\frac{37}{9} = -4\frac{1}{9} \approx -4.111111111$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 2,5,3.

$$15\left(x-3\right)-6\left(x+3\right)=-100$$

Use the distributive property to multiply 15 by x-3.

$$15x-45-6\left(x+3\right)=-100$$

Use the distributive property to multiply -6 by x+3.

$$15x-45-6x-18=-100$$

Combine 15x and -6x to get 9x.

$$9x-45-18=-100$$

Subtract 18 from -45 to get -63.

$$9x-63=-100$$

Add 63 to both sides.

$$9x=-100+63$$

Add -100 and 63 to get -37.

$$9x=-37$$

Divide both sides by 9.

$$x=\frac{-37}{9}$$

Fraction \frac{-37}{9} can be rewritten as -\frac{37}{9} by extracting the negative sign.

$$x=-\frac{37}{9}$$