Solve the following inequality. Click Here for help Video

Question

−
5
6
y

≤
2
6
−5
​
y ≤2

y
y

Answer 1

To solve the inequality \(-\frac{5}{6}y \leq 2\), we will isolate the variable \(y\).

1. Multiply both sides by -6/5: Since we are multiplying by a negative number, we need to flip the inequality sign.

\[ y \geq 2 \cdot \left(-\frac{6}{5}\right) \]

2. Calculating the right side:

\[ 2 \cdot \left(-\frac{6}{5}\right) = -\frac{12}{5} \]

So now we have:

\[ y \geq -\frac{12}{5} \]

3. Final solution:

Thus, the solution to the inequality \(-\frac{5}{6}y \leq 2\) is:

\[ y \geq -\frac{12}{5} \]

or in interval notation:

\[ \left[-\frac{12}{5}, \infty\right) \]