Solve 4/7+3/x+3=5/3

$$\frac { 4 } { 7 } + \frac { 3 } { x + 3 } = \frac { 5 } { 3 }$$

Solve for x

$$x=-\frac{6}{23}\approx -0.260869565$$

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 21\left(x+3\right), the least common multiple of 7,x+3,3.

$$21\left(x+3\right)\times \frac{4}{7}+21\times 3=35\left(x+3\right)$$

Use the distributive property to multiply 21 by x+3.

$$\left(21x+63\right)\times \frac{4}{7}+21\times 3=35\left(x+3\right)$$

Use the distributive property to multiply 21x+63 by \frac{4}{7}.

$$12x+36+21\times 3=35\left(x+3\right)$$

Multiply 21 and 3 to get 63.

$$12x+36+63=35\left(x+3\right)$$

Add 36 and 63 to get 99.

$$12x+99=35\left(x+3\right)$$

Use the distributive property to multiply 35 by x+3.

$$12x+99=35x+105$$

Subtract 35x from both sides.

$$12x+99-35x=105$$

Combine 12x and -35x to get -23x.

$$-23x+99=105$$

Subtract 99 from both sides.

$$-23x=105-99$$

Subtract 99 from 105 to get 6.

$$-23x=6$$

Divide both sides by -23.

$$x=\frac{6}{-23}$$

Fraction \frac{6}{-23} can be rewritten as -\frac{6}{23} by extracting the negative sign.

$$x=-\frac{6}{23}$$