Given the inequality [tex]6x \leq 18[/tex], which of the following is a solution that makes the inequality true?

A. [tex]S: \{26\}[/tex]
B. [tex]S: \{14\}[/tex]
C. [tex]S: \{7\}[/tex]
D. [tex]S: \{3\}[/tex]



Answer :

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]