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

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

Solve for x

$$x\leq -27$$

Solution Steps

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

$$3\left(x-3\right)-2\left(2x+3\right)\geq 12$$

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

$$3x-9-2\left(2x+3\right)\geq 12$$

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

$$3x-9-4x-6\geq 12$$

Combine 3x and -4x to get -x.

$$-x-9-6\geq 12$$

Subtract 6 from -9 to get -15.

$$-x-15\geq 12$$

Add 15 to both sides.

$$-x\geq 12+15$$

Add 12 and 15 to get 27.

$$-x\geq 27$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\leq -27$$