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Match the solution set given in inequality notation with the solution set given in interval notation.

1. [tex]\( x \ \textless \ 78 \)[/tex] --- [tex]\( (-\infty, 78) \)[/tex]

2. [tex]\( x \leq 78 \)[/tex] --- [tex]\( (-\infty, 78] \)[/tex]

3. [tex]\( x \ \textgreater \ 78 \)[/tex] --- [tex]\( (78, \infty) \)[/tex]

Sagot :

GinnyAnsweridn
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]
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