Answered

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Given: [tex]x-8 \ \textgreater \ -3[/tex]

Choose the solution set:

A. [tex]\{x \mid x \in \mathbb{R}, x \ \textgreater \ -5\}[/tex]
B. [tex]\{x \mid x \in \mathbb{R}, x \ \textgreater \ -9\}[/tex]
C. [tex]\{x \mid x \in \mathbb{R}, x \ \textgreater \ 5\}[/tex]
D. [tex]\{x \mid x \in \mathbb{R}, x \ \textgreater \ 14\}[/tex]

Sagot :

GinnyAnsweridn
Let's solve the given inequality step-by-step:

Given:
[tex]\[ x - 8 > -3 \][/tex]

1. First, isolate the variable [tex]\( x \)[/tex] by adding 8 to both sides of the inequality:
[tex]\[ x - 8 + 8 > -3 + 8 \][/tex]
[tex]\[ x > 5 \][/tex]

So, the solution to the inequality [tex]\( x - 8 > -3 \)[/tex] is:
[tex]\[ x > 5 \][/tex]

In set notation, the solution set is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x > 5 \} \][/tex]

Now let's choose the correct solution set from the given options:

1. [tex]\(\{ x \mid x \in R, x > -5 \}\)[/tex]
2. [tex]\(\{ x \mid x \in R, x > -9 \}\)[/tex]
3. [tex]\(\{ x \mid x \in R, x > 5 \}\)[/tex]
4. [tex]\(\{ x \mid x \in R, x > 14 \}\)[/tex]

The correct solution set is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x > 5 \} \][/tex]

Thus, the answer is:
[tex]\[ \{ x \mid x \in R, x > 5 \} \][/tex]
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