Solve 2x+1/5leq3x-2

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

Solve for x

$$x\geq \frac{11}{13}$$

Solution Steps

Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.

$$2x+1\leq 15x-10$$

Subtract 15x from both sides.

$$2x+1-15x\leq -10$$

Combine 2x and -15x to get -13x.

$$-13x+1\leq -10$$

Subtract 1 from both sides.

$$-13x\leq -10-1$$

Subtract 1 from -10 to get -11.

$$-13x\leq -11$$

Divide both sides by -13. Since -13 is negative, the inequality direction is changed.

$$x\geq \frac{-11}{-13}$$

Fraction \frac{-11}{-13} can be simplified to \frac{11}{13} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{11}{13}$$