Question

solve the inequality for y.
3 - \frac{7}{4}y \geq 2y + \frac{1}{6}
simplify your answer as much as possible.

Explanation:

Step1: Eliminate fractions by multiplying all terms by 12 (LCM of 4 and 6)

Multiply each term: \(12\times3 - 12\times\frac{7}{4}y \geq 12\times2y + 12\times\frac{1}{6}\)
Simplify: \(36 - 21y \geq 24y + 2\)

Step2: Move all y terms to one side and constants to the other

Add \(21y\) to both sides: \(36 \geq 24y + 21y + 2\)
Subtract 2 from both sides: \(36 - 2 = 45y\)
Simplify: \(34 \geq 45y\) (or \(45y \leq 34\))

Step3: Solve for y by dividing both sides by 45

\(y \leq \frac{34}{45}\)

Answer:

\(y \leq \frac{34}{45}\)