Certainly! Let's solve the inequality step by step and determine which value from the given sets satisfies the inequality [tex]\(6x \leq 18\)[/tex].
1. Solve the inequality:
Given the inequality [tex]\(6x \leq 18\)[/tex], we need to isolate [tex]\(x\)[/tex]. We do this by dividing both sides of the inequality by 6:
[tex]\[
\frac{6x}{6} \leq \frac{18}{6}
\][/tex]
Simplifying this, we get:
[tex]\[
x \leq 3
\][/tex]
2. Check the values from the sets to see if they satisfy the inequality [tex]\(x \leq 3\)[/tex]:
- For the set [tex]\( S1 = \{26\} \)[/tex]:
[tex]\[
26 \leq 3 \quad \text{(False)}
\][/tex]
- For the set [tex]\( S2 = \{14\} \)[/tex]:
[tex]\[
14 \leq 3 \quad \text{(False)}
\][/tex]
- For the set [tex]\( S3 = \{7\} \)[/tex]:
[tex]\[
7 \leq 3 \quad \text{(False)}
\][/tex]
- For the set [tex]\( S4 = \{3\} \)[/tex]:
[tex]\[
3 \leq 3 \quad \text{(True)}
\][/tex]
Therefore, the value that makes the inequality [tex]\( 6x \leq 18 \)[/tex] true is from the set [tex]\( S4 \)[/tex], which is [tex]\( \{3\} \)[/tex].
The result is:
[tex]\[ \{3\} \][/tex]
