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

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

Solve for x

$$x\geq \frac{13}{4}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$6-\left(2x-5\right)\leq 2x-2$$

To find the opposite of 2x-5, find the opposite of each term.

$$6-2x-\left(-5\right)\leq 2x-2$$

The opposite of -5 is 5.

$$6-2x+5\leq 2x-2$$

Add 6 and 5 to get 11.

$$11-2x\leq 2x-2$$

Subtract 2x from both sides.

$$11-2x-2x\leq -2$$

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

$$11-4x\leq -2$$

Subtract 11 from both sides.

$$-4x\leq -2-11$$

Subtract 11 from -2 to get -13.

$$-4x\leq -13$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

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

Fraction \frac{-13}{-4} can be simplified to \frac{13}{4} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{13}{4}$$