Solve x+1/2leqx+0.5/3

$$\frac{ x+1 }{ 2 } \leq \frac{ x+0.5 }{ 3 }$$

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.

$$3\left(x+1\right)\leq 2\left(x+0.5\right)$$

Use the distributive property to multiply 3 by x+1.

$$3x+3\leq 2\left(x+0.5\right)$$

Use the distributive property to multiply 2 by x+0.5.

$$3x+3\leq 2x+1$$

Subtract 2x from both sides.

$$3x+3-2x\leq 1$$

Combine 3x and -2x to get x.

$$x+3\leq 1$$

Subtract 3 from both sides.

$$x\leq 1-3$$

Subtract 3 from 1 to get -2.

$$x\leq -2$$