Solve y+1/6-2y-5/4geq1

$$\frac{ y+1 }{ 6 } - \frac{ 2y-5 }{ 4 } \geq 1$$

Solve for y

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

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.

$$2\left(y+1\right)-3\left(2y-5\right)\geq 12$$

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

$$2y+2-3\left(2y-5\right)\geq 12$$

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

$$2y+2-6y+15\geq 12$$

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

$$-4y+2+15\geq 12$$

Add 2 and 15 to get 17.

$$-4y+17\geq 12$$

Subtract 17 from both sides.

$$-4y\geq 12-17$$

Subtract 17 from 12 to get -5.

$$-4y\geq -5$$

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

$$y\leq \frac{-5}{-4}$$

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

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