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6. Find the possible values of [tex]$r$[/tex] in the inequality [tex]$5 \ \textgreater \ r - 3$[/tex].

A. [tex][tex]$r \ \textless \ 8$[/tex][/tex]
B. [tex]$r = 2$[/tex]
C. [tex]$r = 8$[/tex]
D. [tex][tex]$r \ \textless \ 2$[/tex][/tex]

Sagot :

GinnyAnswer
To solve the inequality [tex]\(5 > r - 3\)[/tex], let's go through a step-by-step process:

1. Write down the given inequality:
[tex]\[ 5 > r - 3 \][/tex]

2. Isolate [tex]\(r\)[/tex] on one side of the inequality:
- To isolate [tex]\(r\)[/tex], we need to get rid of [tex]\(-3\)[/tex] on the right-hand side. We can do this by adding [tex]\(3\)[/tex] to both sides of the inequality.

3. Perform the addition on both sides:
[tex]\[ 5 + 3 > r - 3 + 3 \][/tex]

4. Simplify the inequality:
- The [tex]\(-3\)[/tex] and [tex]\(+3\)[/tex] on the right-hand side cancel each other out, leaving:
[tex]\[ 8 > r \][/tex]

5. Rewriting the inequality:
[tex]\[ r < 8 \][/tex]

This simplified form tells us that [tex]\(r\)[/tex] must be less than 8. Therefore, the correct answer is:

A. [tex]\(r < 8\)[/tex]
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