Solve 3/2=6-x+10/x-3

$$\frac { 3 } { 2 } = 6 - \frac { x + 10 } { x - 3 }$$

Solve for x

$$x = \frac{47}{7} = 6\frac{5}{7} \approx 6.714285714$$

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 2\left(x-3\right), the least common multiple of 2,x-3.

$$3\left(x-3\right)=2\left(x-3\right)\times 6-2\left(x+10\right)$$

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

$$3x-9=2\left(x-3\right)\times 6-2\left(x+10\right)$$

Multiply 2 and 6 to get 12.

$$3x-9=12\left(x-3\right)-2\left(x+10\right)$$

Use the distributive property to multiply 12 by x-3.

$$3x-9=12x-36-2\left(x+10\right)$$

Use the distributive property to multiply -2 by x+10.

$$3x-9=12x-36-2x-20$$

Combine 12x and -2x to get 10x.

$$3x-9=10x-36-20$$

Subtract 20 from -36 to get -56.

$$3x-9=10x-56$$

Subtract 10x from both sides.

$$3x-9-10x=-56$$

Combine 3x and -10x to get -7x.

$$-7x-9=-56$$

Add 9 to both sides.

$$-7x=-56+9$$

Add -56 and 9 to get -47.

$$-7x=-47$$

Divide both sides by -7.

$$x=\frac{-47}{-7}$$

Fraction \frac{-47}{-7} can be simplified to \frac{47}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{47}{7}$$