Solve x+5/2leq3x+2

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

Solve for x

$$x\geq \frac{1}{5}$$

Solution Steps

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

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

Subtract 6x from both sides.

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

Combine x and -6x to get -5x.

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

Subtract 5 from both sides.

$$-5x\leq 4-5$$

Subtract 5 from 4 to get -1.

$$-5x\leq -1$$

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

$$x\geq \frac{-1}{-5}$$

Fraction \frac{-1}{-5} can be simplified to \frac{1}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{1}{5}$$