Certainly! Let's match the given inequalities with their corresponding interval notations:
1. Inequality: [tex]\( x < 78 \)[/tex]
For the inequality [tex]\( x < 78 \)[/tex], the solution includes all numbers less than 78 but not including 78 itself. In interval notation, this is represented as:
[tex]\[ (-\infty, 78) \][/tex]
This interval includes all real numbers that are less than 78 but excludes 78.
2. Inequality: [tex]\( x \leq 78 \)[/tex]
For the inequality [tex]\( x \leq 78 \)[/tex], the solution includes all numbers less than or equal to 78. In interval notation, this is represented as:
[tex]\[ (-\infty, 78] \][/tex]
This interval includes all real numbers that are less than 78 and also includes 78 itself.
3. Inequality: [tex]\( x > 78 \)[/tex]
For the inequality [tex]\( x > 78 \)[/tex], the solution includes all numbers greater than 78. In interval notation, this is represented as:
[tex]\[ (78, \infty) \][/tex]
This interval includes all real numbers greater than 78 but excludes 78 itself.
So the matches are:
[tex]\[
\begin{aligned}
&x < 78 &\longrightarrow &&(-\infty, 78) \\
&x \leq 78 &\longrightarrow &&(-\infty, 78] \\
&x > 78 &\longrightarrow &&(78, \infty) \\
\end{aligned}
\][/tex]
