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

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

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2x,2.

$$-\left(x-5\right)+2x\left(-1\right)=3x$$

To find the opposite of x-5, find the opposite of each term.

$$-x+5+2x\left(-1\right)=3x$$

Multiply 2 and -1 to get -2.

$$-x+5-2x=3x$$

Combine -x and -2x to get -3x.

$$-3x+5=3x$$

Subtract 3x from both sides.

$$-3x+5-3x=0$$

Combine -3x and -3x to get -6x.

$$-6x+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-6x=-5$$

Divide both sides by -6.

$$x=\frac{-5}{-6}$$

Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{6}$$