Solve x-3/2geq2x-5/3

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

Solve for x

$$x\leq 1$$

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.

$$3\left(x-3\right)\geq 2\left(2x-5\right)$$

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

$$3x-9\geq 2\left(2x-5\right)$$

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

$$3x-9\geq 4x-10$$

Subtract 4x from both sides.

$$3x-9-4x\geq -10$$

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

$$-x-9\geq -10$$

Add 9 to both sides.

$$-x\geq -10+9$$

Add -10 and 9 to get -1.

$$-x\geq -1$$

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

$$x\leq \frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$x\leq 1$$