Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the best answer for the question.

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

A. [tex]x \ \textgreater \ 5[/tex]

B. [tex]x \ \textgreater \ -8[/tex]

C. [tex]x \ \textless \ 8[/tex]

D. [tex]x \ \textless \ -2[/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\(-122 < -3(-2 - 8x) - 8x\)[/tex], let's go through the steps methodically:

1. Distribute and Simplify the Expression:

Begin by distributing the [tex]\(-3\)[/tex] inside the parentheses:

[tex]\[ -122 < -3(-2 - 8x) - 8x \][/tex]

[tex]\[ -122 < (-3 \cdot -2) + (-3 \cdot -8x) - 8x \][/tex]

This gives us:

[tex]\[ -122 < 6 + 24x - 8x \][/tex]

2. Combine Like Terms:

Now combine the terms involving [tex]\(x\)[/tex]:

[tex]\[ -122 < 6 + 16x \][/tex]

3. Isolate the Variable Term:

Subtract 6 from both sides to begin isolating the term with [tex]\(x\)[/tex]:

[tex]\[ -128 < 16x \][/tex]

4. Solve for [tex]\(x\)[/tex]:

Finally, divide both sides by 16 to solve for [tex]\(x\)[/tex]:

[tex]\[ \frac{-128}{16} < x \][/tex]

[tex]\[ -8 < x \][/tex]

This inequality tells us that [tex]\(x\)[/tex] must be greater than [tex]\(-8\)[/tex].

So the solution to the inequality [tex]\(-122 < -3(-2 - 8x) - 8x\)[/tex] is:

[tex]\[ x > -8 \][/tex]

The best answer from the given options is:

B. [tex]\( x > -8 \)[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.