Solve x+5/2-1leq3x+2/2

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

Solve for x

$$x\geq \frac{1}{2}$$

Solution Steps

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

$$x+5-2\leq 3x+2$$

Subtract 2 from 5 to get 3.

$$x+3\leq 3x+2$$

Subtract 3x from both sides.

$$x+3-3x\leq 2$$

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

$$-2x+3\leq 2$$

Subtract 3 from both sides.

$$-2x\leq 2-3$$

Subtract 3 from 2 to get -1.

$$-2x\leq -1$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x\geq \frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{2}$$