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Given: [tex]-6x \ \textless \ 36[/tex].

Choose the solution set.
A. [tex]\{x \mid x \ \textless \ -6\}[/tex]
B. [tex]\{x \mid x \ \textgreater \ 6\}[/tex]
C. [tex]\{x \mid x \ \textgreater \ -6\}[/tex]
D. [tex]\{x \mid x \ \textless \ 6\}[/tex]

Sagot :

GinnyAnsweridn
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.
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