Solve -6=3/4-5-2/x-5

$$-6= \frac{ 3 }{ 4 } - \frac{ 5-2 }{ x-5 }$$

Solve for x

$$x = \frac{49}{9} = 5\frac{4}{9} \approx 5.444444444$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 4\left(x-5\right), the least common multiple of 4,x-5.

$$-24\left(x-5\right)=4\left(x-5\right)\times \frac{3}{4}-4\left(5-2\right)$$

Use the distributive property to multiply -24 by x-5.

$$-24x+120=4\left(x-5\right)\times \frac{3}{4}-4\left(5-2\right)$$

Multiply 4 and \frac{3}{4} to get 3.

$$-24x+120=3\left(x-5\right)-4\left(5-2\right)$$

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

$$-24x+120=3x-15-4\left(5-2\right)$$

Subtract 2 from 5 to get 3.

$$-24x+120=3x-15-4\times 3$$

Multiply -4 and 3 to get -12.

$$-24x+120=3x-15-12$$

Subtract 12 from -15 to get -27.

$$-24x+120=3x-27$$

Subtract 3x from both sides.

$$-24x+120-3x=-27$$

Combine -24x and -3x to get -27x.

$$-27x+120=-27$$

Subtract 120 from both sides.

$$-27x=-27-120$$

Subtract 120 from -27 to get -147.

$$-27x=-147$$

Divide both sides by -27.

$$x=\frac{-147}{-27}$$

Reduce the fraction \frac{-147}{-27} to lowest terms by extracting and canceling out -3.

$$x=\frac{49}{9}$$