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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]
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