Solve x+2/3geq2x-3/2

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

Solve for x

$$x\leq \frac{13}{4}$$

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.

$$2\left(x+2\right)\geq 3\left(2x-3\right)$$

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

$$2x+4\geq 3\left(2x-3\right)$$

Use the distributive property to multiply 3 by 2x-3.

$$2x+4\geq 6x-9$$

Subtract 6x from both sides.

$$2x+4-6x\geq -9$$

Combine 2x and -6x to get -4x.

$$-4x+4\geq -9$$

Subtract 4 from both sides.

$$-4x\geq -9-4$$

Subtract 4 from -9 to get -13.

$$-4x\geq -13$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\leq \frac{-13}{-4}$$

Fraction \frac{-13}{-4} can be simplified to \frac{13}{4} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{13}{4}$$