Solve 1/x+3+2/3=8

$$\frac { 1 } { x + 3 } + \frac { 2 } { 3 } = 8$$

Solve for x

$$x = -\frac{63}{22} = -2\frac{19}{22} \approx -2.863636364$$

Steps for Solving Linear Equation

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+3\right), the least common multiple of x+3,3.

$$3+3\left(x+3\right)\times \frac{2}{3}=24\left(x+3\right)$$

Multiply 3 and \frac{2}{3} to get 2.

$$3+2\left(x+3\right)=24\left(x+3\right)$$

Use the distributive property to multiply 2 by x+3.

$$3+2x+6=24\left(x+3\right)$$

Add 3 and 6 to get 9.

$$9+2x=24\left(x+3\right)$$

Use the distributive property to multiply 24 by x+3.

$$9+2x=24x+72$$

Subtract 24x from both sides.

$$9+2x-24x=72$$

Combine 2x and -24x to get -22x.

$$9-22x=72$$

Subtract 9 from both sides.

$$-22x=72-9$$

Subtract 9 from 72 to get 63.

$$-22x=63$$

Divide both sides by -22.

$$x=\frac{63}{-22}$$

Fraction \frac{63}{-22} can be rewritten as -\frac{63}{22} by extracting the negative sign.

$$x=-\frac{63}{22}$$