Solve x+1/4leqx-3/-6

$$\frac{ x+1 }{ 4 } \leq \frac{ x-3 }{ -6 }$$

Solve for x

$$x\leq \frac{3}{5}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,-6. Since 12 is positive, the inequality direction remains the same.

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

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

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

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

$$3x+3\leq -2x+6$$

Add 2x to both sides.

$$3x+3+2x\leq 6$$

Combine 3x and 2x to get 5x.

$$5x+3\leq 6$$

Subtract 3 from both sides.

$$5x\leq 6-3$$

Subtract 3 from 6 to get 3.

$$5x\leq 3$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\leq \frac{3}{5}$$