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Solve the following inequality for [tex]r[/tex]. Write your answer in simplest form.

[tex]-10r - 3 \geq 10r + 6[/tex]

Answer :

Sure! Let's solve the inequality step-by-step:

We have the inequality:
[tex]\[
-10r - 3 \geq 10r + 6
\][/tex]

Step 1: Move terms involving [tex]\( r \)[/tex] to one side

First, add [tex]\( 10r \)[/tex] to both sides to get all the [tex]\( r \)[/tex] terms on one side:
[tex]\[
-10r + 10r - 3 \geq 10r + 10r + 6
\][/tex]

This simplifies to:
[tex]\[
-3 \geq 20r + 6
\][/tex]

Step 2: Move constant terms to the other side

Next, subtract 6 from both sides to isolate the terms involving [tex]\( r \)[/tex]:
[tex]\[
-3 - 6 \geq 20r
\][/tex]

Simplify the left side:
[tex]\[
-9 \geq 20r
\][/tex]

Step 3: Solve for [tex]\( r \)[/tex]

Now, divide both sides by 20 to solve for [tex]\( r \)[/tex]:
[tex]\[
r \leq -\frac{9}{20}
\][/tex]

So, the solution to the inequality is:
[tex]\[
r \leq -\frac{9}{20}
\][/tex]

This means that [tex]\( r \)[/tex] can be any value less than or equal to [tex]\(-\frac{9}{20}\)[/tex].

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