Question
Solve the following inequality. Click Here for help Video
−
5
6
y
≤
2
6
−5
y ≤2
y
y
Answers
GPT-4o mini
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:
\[
\left[-\frac{12}{5}, \infty\right)
\]
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:
\[
\left[-\frac{12}{5}, \infty\right)
\]