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anonymous
 one year ago
Solve and graph the absolute value inequality: 4x + 1 ≤ 5.
anonymous
 one year ago
Solve and graph the absolute value inequality: 4x + 1 ≤ 5.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I can help you with this. First of all, the "4x + 1" inside is making it look harder than it really is. So, let's start a bit easier. Are you able to solve \(x\le 5\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure how to solve that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, let's start there then. So many people get really confused by absolute value inequalities because they try to memorize lots of different formulas (yuck). Instead, remember that absolute value means distance from zero.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When you say 3 = 3, here's what's going on: 3 is asking: "How far away from 0 is the number 3?" The answer is of course 3.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When you say 3 = 3, here's what's going on: 3 is asking: How far from 0 is the number 3" The answer is AGAIN 3. Does this make sense so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah that makes perfect sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Awesome. So, now, if I ask you to solve x = 3, here's what you want to think: What numbers (we're calling them x) have a DISTANCE FROM ZERO that is equal to 3. Can you tell me the answer? (Remember ... you can walk away from zero in two directions.)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is *one* of the numbers that is three units from zero. Is there another one?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes! So, the solution to x = 3 is: x = 3 or x = 3 Now, let's go on to the type that you're actually interested in...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When you see \(x\le 3\), you're really being asked: What are all the numbers whose *distance from zero* is *less than or equal to 3*.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, I want you to imagine yourself standing at zero on a number line. (Maybe this is your "home", and you're driving your Mom crazy!)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So your Mom says: please go away for while! But, don't go TOO FAR ... I don't want you to go any more than 3 (miles, maybe) away. Now, you can head out your front door and turn right, or turn left. But, you can't go more than 3 away. What numbers can you visit?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahhh... you're getting close! Let me ask you this. Can you visit 1.5? Can you visit 2.5?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right! So, remember, the instructions are: go \(\le\) 3 (miles) away. Can you revise your answer? What neighbors (numbers) can you visit?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Feel free to use words to give your answer for now, like "all the numbers between blah and blah".

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Are you there? Do you want a hint?

marcelie
 one year ago
Best ResponseYou've already chosen the best response.0there are many ways to solve it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think he/she may be gone. I've got to get going, so I'll let you take over. I was getting them to the fact that the solution of \(x \le 3\) is \(3 \le x \le 3\). Have a great day!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you come back, this page might be helpful: http://www.onemathematicalcat.org/algebra_book/online_problems/solve_simple_abs_val_sen.htm Then, there are also pages for more advanced problems.
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