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

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

Solve for x

$$x=-\frac{4}{11}\approx -0.363636364$$

Steps for Solving Linear Equation

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

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

Multiply -3 and 5 to get -15.

$$6x-15x=2\left(x+2\right)$$

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

$$-9x=2\left(x+2\right)$$

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

$$-9x=2x+4$$

Subtract 2x from both sides.

$$-9x-2x=4$$

Combine -9x and -2x to get -11x.

$$-11x=4$$

Divide both sides by -11.

$$x=\frac{4}{-11}$$

Fraction \frac{4}{-11} can be rewritten as -\frac{4}{11} by extracting the negative sign.

$$x=-\frac{4}{11}$$