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Solve [tex]\(-2x - 8 \ \textgreater \ 5x + 13\)[/tex].

A. [tex]\(x \ \textless \ -3\)[/tex]
B. [tex]\(x \ \textgreater \ -3\)[/tex]
C. [tex]\(x \ \textless \ -7\)[/tex]
D. [tex]\(x \ \textgreater \ -7\)[/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\(-2x - 8 > 5x + 13\)[/tex], follow these steps:

1. Isolate the variable on one side:

Start by moving all terms involving [tex]\(x\)[/tex] to one side of the inequality and constants to the other side. Subtract [tex]\(5x\)[/tex] from both sides:
[tex]\[ -2x - 8 - 5x > 5x + 13 - 5x \][/tex]

2. Combine like terms:

Simplify the inequality by combining the [tex]\(x\)[/tex] terms on the left side and the constants on the right side:
[tex]\[ -7x - 8 > 13 \][/tex]

3. Isolate the [tex]\(x\)[/tex] term:

Add [tex]\(8\)[/tex] to both sides of the inequality to move the constants to one side:
[tex]\[ -7x - 8 + 8 > 13 + 8 \][/tex]
[tex]\[ -7x > 21 \][/tex]

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

Finally, divide both sides by [tex]\(-7\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[ -7x / -7 < 21 / -7 \][/tex]
[tex]\[ x < -3 \][/tex]

Therefore, the solution to the inequality [tex]\(-2x - 8 > 5x + 13\)[/tex] is [tex]\(\boxed{x < -3}\)[/tex].

This corresponds to choice A.
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