Solve 2x-(4x-5)geqx

$$2x-(4x-5) \geq x$$

Solve for x

$$x\leq \frac{5}{3}$$

Solution Steps

To find the opposite of 4x-5, find the opposite of each term.

$$2x-4x-\left(-5\right)\geq x$$

The opposite of -5 is 5.

$$2x-4x+5\geq x$$

Combine 2x and -4x to get -2x.

$$-2x+5\geq x$$

Subtract x from both sides.

$$-2x+5-x\geq 0$$

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

$$-3x+5\geq 0$$

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

$$-3x\geq -5$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x\leq \frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{5}{3}$$