To solve the inequality [tex]\(-6x < 36\)[/tex], let's go through the steps methodically:
1. Identify the inequality: The given inequality is:
[tex]\[ -6x < 36 \][/tex]
2. Isolate [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], we need to divide both sides of the inequality by [tex]\(-6\)[/tex]. It's very important to remember that when we divide by a negative number, the direction of the inequality sign must be reversed.
[tex]\[ -6x < 36 \][/tex]
Dividing both sides by [tex]\(-6\)[/tex]:
[tex]\[ x > \frac{36}{-6} \][/tex]
3. Simplify the fraction: Simplify [tex]\(\frac{36}{-6}\)[/tex]:
[tex]\[ x > -6 \][/tex]
So, the solution set for the inequality [tex]\(-6x < 36\)[/tex] is:
[tex]\[ \{ x \mid x > -6 \} \][/tex]
Among the provided options, the correct one is:
[tex]\[ \{ x \mid x > -6 \} \][/tex]
Thus, the correct solution set is [tex]\(\{x \mid x > -6\}\)[/tex], corresponding to the third choice in the given options.
