Solve x+5/2=1-x-x-2/3

$$\frac{ x+5 }{ 2 } = 1-x- \frac{ x-2 }{ 3 }$$

Solve for x

$$x=-\frac{5}{11}\approx -0.454545455$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 3 by x+5.

$$3x+15=6-6x-2\left(x-2\right)$$

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

$$3x+15=6-6x-2x+4$$

Combine -6x and -2x to get -8x.

$$3x+15=6-8x+4$$

Add 6 and 4 to get 10.

$$3x+15=10-8x$$

Add 8x to both sides.

$$3x+15+8x=10$$

Combine 3x and 8x to get 11x.

$$11x+15=10$$

Subtract 15 from both sides.

$$11x=10-15$$

Subtract 15 from 10 to get -5.

$$11x=-5$$

Divide both sides by 11.

$$x=\frac{-5}{11}$$

Fraction \frac{-5}{11} can be rewritten as -\frac{5}{11} by extracting the negative sign.

$$x=-\frac{5}{11}$$