Alaina257
Answered

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12. What is the solution to [tex]-122 \ \textless \ -3(-2 - 8x) - 8x[/tex]?

A. [tex]x \ \textless \ -2[/tex]
B. [tex]x \ \textless \ 8[/tex]
C. [tex]x \ \textgreater \ -8[/tex]
D. [tex]x \ \textgreater \ 5[/tex]

Sagot :

GinnyAnswer
Let's solve the inequality step-by-step.

We start with the inequality:
[tex]\[ -122 < -3(-2 - 8x) - 8x \][/tex]

First, we need to distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[ -3(-2 - 8x) = -3 \cdot (-2) - 3 \cdot (8x) = 6 + 24x \][/tex]
So the inequality becomes:
[tex]\[ -122 < 6 + 24x - 8x \][/tex]

Next, we combine like terms:
[tex]\[ 24x - 8x = 16x \][/tex]
So the inequality is now:
[tex]\[ -122 < 6 + 16x \][/tex]

Our next step is to isolate the term containing [tex]\(x\)[/tex]. We do this by subtracting 6 from both sides:
[tex]\[ -122 - 6 < 16x \implies -128 < 16x \][/tex]

Now, we divide both sides by 16 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{-128}{16} < x \implies -8 < x \][/tex]

This can also be written as:
[tex]\[ x > -8 \][/tex]

Thus, the solution to the inequality [tex]\( -122 < -3(-2 - 8x) - 8x \)[/tex] is:
[tex]\[ \boxed{x > -8} \][/tex]

So, the correct answer is:
C. [tex]\( x > -8 \)[/tex]
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