Solve 2x+5/3leq3x-1/2

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

Solve for x

$$x\geq \frac{13}{5}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x+5\right)\leq 3\left(3x-1\right)$$

Use the distributive property to multiply 2 by 2x+5.

$$4x+10\leq 3\left(3x-1\right)$$

Use the distributive property to multiply 3 by 3x-1.

$$4x+10\leq 9x-3$$

Subtract 9x from both sides.

$$4x+10-9x\leq -3$$

Combine 4x and -9x to get -5x.

$$-5x+10\leq -3$$

Subtract 10 from both sides.

$$-5x\leq -3-10$$

Subtract 10 from -3 to get -13.

$$-5x\leq -13$$

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

$$x\geq \frac{-13}{-5}$$

Fraction \frac{-13}{-5} can be simplified to \frac{13}{5} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{13}{5}$$