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Solve the inequality [tex]\frac{1}{3} y \ \textgreater \ -2[/tex].

[tex]\[
\begin{array}{c}
\frac{1}{3} y \ \textgreater \ -2 \\
3 \left( \frac{1}{3} y \right) \ \textgreater \ 3 (-2) \quad \text{Multiply by 3 on both sides. Do not reverse the inequality.} \\
y \ \textgreater \ \square
\end{array}
\][/tex]

Fill in the blank with the correct value.

Sagot :

GinnyAnsweridn
To solve the inequality [tex]\(\frac{1}{3} y > -2\)[/tex], we need to isolate the variable [tex]\(y\)[/tex]. Here is a step-by-step solution:

1. Start with the inequality:
[tex]\[ \frac{1}{3} y > -2 \][/tex]

2. Multiply both sides by 3 to eliminate the fraction. It's important to note that multiplying or dividing both sides of an inequality by a positive number does not reverse the inequality sign. So, we have:
[tex]\[ 3 \left( \frac{1}{3} y \right) > 3 (-2) \][/tex]

3. Simplify both sides:
[tex]\[ y > -6 \][/tex]

Therefore, the solution to the inequality [tex]\(\frac{1}{3} y > -2\)[/tex] is:
[tex]\[ y > -6 \][/tex]
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