Let's match each inequality to its corresponding solution:
For the inequality [tex]\(2(5)^z > 250\)[/tex]:
- The solution is [tex]\(z > 3\)[/tex].
- So, [tex]\(2(5)^z > 250 \longrightarrow x > 3\)[/tex].
For the inequality [tex]\(4\left(\frac{1}{3}\right)^2 < 36\)[/tex]:
- This inequality does not provide a specific solution for [tex]\(x\)[/tex].
- So, [tex]\(4\left(\frac{1}{3}\right)^2<36 \longrightarrow \text{No specific solution}\)[/tex].
For the inequality [tex]\(10\left(\frac{1}{2}\right)^x > 80\)[/tex]:
- The solution is [tex]\(x > 3\)[/tex].
- So, [tex]\(10\left(\frac{1}{2}\right)^x > 80 \longrightarrow x > 3\)[/tex].
For the inequality [tex]\(\left(\frac{1}{2}\right)(6)^x < 18\)[/tex]:
- The solution is [tex]\(x < 2\)[/tex].
- So, [tex]\(\left(\frac{1}{2}\right)(6)^x<18 \longrightarrow x < 2\)[/tex].
Considering the given pairs, we have:
[tex]\[
\begin{aligned}
&2(5)^z > 250 \longrightarrow x > 3, \\
&4\left(\frac{1}{3}\right)^2<36 \longrightarrow \text{No specific solution}, \\
&10\left(\frac{1}{2}\right)^x > 80 \longrightarrow x > 3, \\
&\left(\frac{1}{2}\right)(6)^x<18 \longrightarrow x < 2.
\end{aligned}
\][/tex]
Thus, the correct matches are:
- [tex]\(2(5)^z > 250 \longrightarrow x > 3\)[/tex]
- [tex]\(4\left(\frac{1}{3}\right)^2<36 \longrightarrow \text{No specific solution}\)[/tex]
- [tex]\(10\left(\frac{1}{2}\right)^x > 80 \longrightarrow x > 3\)[/tex]
- [tex]\(\left(\frac{1}{2}\right)(6)^x<18 \longrightarrow x < 2\)[/tex]
