Question

solve the inequality for y.
-3y - 14 ≥ 3y + 16
simplify your answer as much as possible.

Explanation:

Step1: Add \(3y\) to both sides

To get all the \(y\)-terms on one side, we add \(3y\) to both sides of the inequality \(-3y - 14\geq3y + 16\). This gives \(-3y+3y - 14\geq3y + 3y+ 16\), which simplifies to \(-14\geq6y + 16\).

Step2: Subtract 16 from both sides

Next, we subtract 16 from both sides to isolate the term with \(y\). So, \(-14-16\geq6y+16 - 16\), which simplifies to \(-30\geq6y\).

Step3: Divide both sides by 6

Now, we divide both sides by 6 to solve for \(y\). Remember that when dividing an inequality by a positive number, the direction of the inequality sign remains the same. So, \(\frac{-30}{6}\geq\frac{6y}{6}\), which simplifies to \(- 5\geq y\) or \(y\leq - 5\).

Answer:

\(y\leq - 5\)