Solve -(x-6)leq4x-5

$$- ( x - 6 ) \leq 4 x - 5$$

Solve for x

$$x\geq \frac{11}{5}$$

Solution Steps

To find the opposite of x-6, find the opposite of each term.

$$-x-\left(-6\right)\leq 4x-5$$

The opposite of -6 is 6.

$$-x+6\leq 4x-5$$

Subtract 4x from both sides.

$$-x+6-4x\leq -5$$

Combine -x and -4x to get -5x.

$$-5x+6\leq -5$$

Subtract 6 from both sides.

$$-5x\leq -5-6$$

Subtract 6 from -5 to get -11.

$$-5x\leq -11$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-11}{-5}$$

Fraction \frac{-11}{-5} can be simplified to \frac{11}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{11}{5}$$