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What is the solution set of this inequality?
[tex]\[ -8x - 1 \ \textgreater \ 3x + 14 \][/tex]

A. [tex]\( x \ \textless \ -3 \)[/tex]
B. [tex]\( x \ \textless \ -\frac{15}{11} \)[/tex]
C. [tex]\( x \ \textgreater \ -3 \)[/tex]
D. [tex]\( x \ \textgreater \ -\frac{15}{11} \)[/tex]


Sagot :

Sure, let's solve the inequality step-by-step to find the correct solution.

Given inequality:
[tex]\[ -8x - 1 > 3x + 14 \][/tex]

First, we'll move all terms involving [tex]\(x\)[/tex] to one side and the constant terms to the other side.

1. Subtract [tex]\(3x\)[/tex] from both sides:
[tex]\[ -8x - 1 - 3x > 14 \][/tex]
This simplifies to:
[tex]\[ -11x - 1 > 14 \][/tex]

2. Next, add 1 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ -11x - 1 + 1 > 14 + 1 \][/tex]
This simplifies to:
[tex]\[ -11x > 15 \][/tex]

3. To solve for [tex]\(x\)[/tex], we need to divide both sides of the inequality by [tex]\(-11\)[/tex]. Remember that dividing or multiplying both sides of an inequality by a negative number reverses the direction of the inequality:
[tex]\[ x < \frac{15}{11} \][/tex]

So, the solution set for the inequality [tex]\(-8x - 1 > 3x + 14\)[/tex] is:
[tex]\[ x < \frac{15}{11} \][/tex]

Among the given choices, this corresponds to:
[tex]\[ x < -\frac{15}{11} \][/tex]

Therefore, the correct answer is:
[tex]\(x < -\frac{15}{11}\)[/tex].
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