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

[tex]\[ 9v - 8 \geq 8v + 2 \][/tex]

Sagot :

GinnyAnswer
Sure, I'd be happy to help!

Let's start with the given inequality:

[tex]\[ 9v - 8 \geq 8v + 2 \][/tex]

Step 1: Subtract [tex]\(8v\)[/tex] from both sides to isolate terms involving [tex]\(v\)[/tex] on one side of the inequality:

[tex]\[ 9v - 8 - 8v \geq 8v + 2 - 8v \][/tex]

This simplifies to:

[tex]\[ v - 8 \geq 2 \][/tex]

Step 2: Add 8 to both sides to isolate [tex]\(v\)[/tex]:

[tex]\[ v - 8 + 8 \geq 2 + 8 \][/tex]

This simplifies to:

[tex]\[ v \geq 10 \][/tex]

So, the solution to the inequality [tex]\( 9v - 8 \geq 8v + 2 \)[/tex] is:

[tex]\[ v \geq 10 \][/tex]

Therefore, the inequality holds true for all values of [tex]\(v\)[/tex] that are greater than or equal to 10.
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