Solve 2-xleq-3x-5/4

$$2 - x \leq - \frac { 3 x - 5 } { 4 }$$

Solve for x

$$x\geq 3$$

Solution Steps

Multiply both sides of the equation by 4. Since 4 is positive, the inequality direction remains the same.

$$8-4x\leq -\left(3x-5\right)$$

To find the opposite of 3x-5, find the opposite of each term.

$$8-4x\leq -3x-\left(-5\right)$$

The opposite of -5 is 5.

$$8-4x\leq -3x+5$$

Add 3x to both sides.

$$8-4x+3x\leq 5$$

Combine -4x and 3x to get -x.

$$8-x\leq 5$$

Subtract 8 from both sides.

$$-x\leq 5-8$$

Subtract 8 from 5 to get -3.

$$-x\leq -3$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq \frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x\geq 3$$