Solve x-4/2leqx-5/3

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

Solve for x

$$x\leq 2$$

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.

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

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

$$3x-12\leq 2\left(x-5\right)$$

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

$$3x-12\leq 2x-10$$

Subtract 2x from both sides.

$$3x-12-2x\leq -10$$

Combine 3x and -2x to get x.

$$x-12\leq -10$$

Add 12 to both sides.

$$x\leq -10+12$$

Add -10 and 12 to get 2.

$$x\leq 2$$