Solve 2x+5/3geq2/3-5/2

$$\frac { 2 x + 5 } { 3 } \geq \frac { 2 } { 3 } - \frac { 5 } { 2 }$$

Solve for x

$$x\geq -\frac{21}{4}$$

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.

$$2\left(2x+5\right)\geq 4-15$$

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

$$4x+10\geq 4-15$$

Subtract 15 from 4 to get -11.

$$4x+10\geq -11$$

Subtract 10 from both sides.

$$4x\geq -11-10$$

Subtract 10 from -11 to get -21.

$$4x\geq -21$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\geq -\frac{21}{4}$$