Solve 2x-5/4+1leqx+1/6

$$\frac { 2 x - 5 } { 4 } + 1 \leq \frac { x + 1 } { 6 }$$

Solve for x

$$x\leq \frac{5}{4}$$

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.

$$3\left(2x-5\right)+12\leq 2\left(x+1\right)$$

Use the distributive property to multiply 3 by 2x-5.

$$6x-15+12\leq 2\left(x+1\right)$$

Add -15 and 12 to get -3.

$$6x-3\leq 2\left(x+1\right)$$

Use the distributive property to multiply 2 by x+1.

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

Subtract 2x from both sides.

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

Combine 6x and -2x to get 4x.

$$4x-3\leq 2$$

Add 3 to both sides.

$$4x\leq 2+3$$

Add 2 and 3 to get 5.

$$4x\leq 5$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\leq \frac{5}{4}$$