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Question:
[tex]\[ 3a \ \textgreater \ a + 8 \][/tex] is equivalent to:

A. [tex]\[ a \ \textgreater \ 8 \][/tex]

B. [tex]\[ a \ \textgreater \ 4 \][/tex]

C. [tex]\[ a \ \textgreater \ 2 \][/tex]

D. [tex]\[ a \ \textgreater \ \frac{3}{8} \][/tex]

Sagot :

GinnyAnsweridn
To solve the inequality [tex]\(3a > a + 8\)[/tex], follow these steps:

1. Isolate the variable on one side:

First, we need to get all the terms involving [tex]\(a\)[/tex] on one side of the inequality and the constants on the other side.

Start by subtracting [tex]\(a\)[/tex] from both sides of the inequality:
[tex]\[ 3a - a > a + 8 - a \][/tex]
This simplifies to:
[tex]\[ 2a > 8 \][/tex]

2. Solve for [tex]\(a\)[/tex]:

Next, we need to solve for [tex]\(a\)[/tex]. To do this, divide both sides of the inequality by 2:
[tex]\[ \frac{2a}{2} > \frac{8}{2} \][/tex]
This simplifies to:
[tex]\[ a > 4 \][/tex]

Therefore, the solution to the inequality [tex]\(3a > a + 8\)[/tex] is [tex]\(a > 4\)[/tex].

So, the correct answer from the given options is:
[tex]\[ a > 4 \][/tex]
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