Solve 2x+1/3-4x+5/2leq0

$$\frac { 2 x + 1 } { 3 } - \frac { 4 x + 5 } { 2 } \leq 0$$

Solve for x

$$x\geq -\frac{13}{8}$$

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.

$$2\left(2x+1\right)-3\left(4x+5\right)\leq 0$$

Use the distributive property to multiply 2 by 2x+1.

$$4x+2-3\left(4x+5\right)\leq 0$$

Use the distributive property to multiply -3 by 4x+5.

$$4x+2-12x-15\leq 0$$

Combine 4x and -12x to get -8x.

$$-8x+2-15\leq 0$$

Subtract 15 from 2 to get -13.

$$-8x-13\leq 0$$

Add 13 to both sides. Anything plus zero gives itself.

$$-8x\leq 13$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x\geq -\frac{13}{8}$$