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What is the solution to 3*|x-4|-5<10

User Gereltod
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1 Answer

7 votes

Answer: x is greater than -1 and less than 9.

Explanation:

Let's solve the inequality step by step:

First, let's isolate the absolute value:

3*|x-4| - 5 < 10

=> 3*|x-4| < 10 + 5

=> 3*|x-4| < 15

Then, we divide both sides by 3 to get:

|x-4| < 15 / 3

=> |x-4| < 5

Now, remember that the definition of |a| < b is -b < a < b, so this becomes:

-5 < x-4 < 5

Next, we solve for x by adding 4 to all sides:

-5 + 4 < x < 5 + 4

So, the solution to the inequality is:

-1 < x < 9

Which means that x is greater than -1 and less than 9

User Nergal
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