Solve 1div-2x-6>6x-4

$$1 \div -2x-6 > 6x-4$$

Solve for x

$$x<-\frac{4}{13}$$

Solution Steps

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}x-6>6x-4$$

Subtract 6x from both sides.

$$-\frac{1}{2}x-6-6x>-4$$

Combine -\frac{1}{2}x and -6x to get -\frac{13}{2}x.

$$-\frac{13}{2}x-6>-4$$

Add 6 to both sides.

$$-\frac{13}{2}x>-4+6$$

Add -4 and 6 to get 2.

$$-\frac{13}{2}x>2$$

Multiply both sides by -\frac{2}{13}, the reciprocal of -\frac{13}{2}. Since -\frac{13}{2} is negative, the inequality direction is changed.

$$x<2\left(-\frac{2}{13}\right)$$

Express 2\left(-\frac{2}{13}\right) as a single fraction.

$$x<\frac{2\left(-2\right)}{13}$$

Multiply 2 and -2 to get -4.

$$x<\frac{-4}{13}$$

Fraction \frac{-4}{13} can be rewritten as -\frac{4}{13} by extracting the negative sign.

$$x<-\frac{4}{13}$$