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

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

Solve for x

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

Solution Steps

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

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

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

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

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

$$2x+2>6x-15+12$$

Add -15 and 12 to get -3.

$$2x+2>6x-3$$

Subtract 6x from both sides.

$$2x+2-6x>-3$$

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

$$-4x+2>-3$$

Subtract 2 from both sides.

$$-4x>-3-2$$

Subtract 2 from -3 to get -5.

$$-4x>-5$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-5}{-4}$$

Fraction \frac{-5}{-4} can be simplified to \frac{5}{4} by removing the negative sign from both the numerator and the denominator.

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