Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i. Let me mark out the 0 a little bit better, so you see relative to 0. So let's just figure out what this graph would look like in general.

So conceptually, it's how far you are away from 0. The absolute value of 4x minus 1, is equal to-- actually, I'll just keep it-- is equal to Remember, up here we said, what are the x's that are exactly 10 away from positive 5?

This number line is the answer to this command up here. If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.

Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.

So you take the absolute value. So that's when x is less than negative 3.

This is because the value inside of the absolute value bars can be positive or negative to result in the same answer. The first way to think about it is, how far is something from 0?

How far is 5 away from 0? And you say, well, it's 1, 2, 3 away from 0. So this graph looks like this strange v.

So then this thing is the same thing as y is equal to x plus 3. So this is equal to positive 4. Add 1 to both sides of this equation-- we could do them simultaneous, even.

Or the thing inside of the absolute value sign, the x plus 2, could also be negative 6. And we have one left. So how many numbers that are exactly 10 away from 5?

When the situation where this-- the inside of our absolute value sign-- is negative, in that situation this equation is going to be y is equal to the negative of x plus 3. Negative 3 sits right over there, so this is negative 3 right there. So how far is 0 from 0? How far is negative 3 from 0?

Well, it's 0 away from 0.

And just as a bit of a review, when you take the absolute value of a number. So on some level, absolute value is the distance from 0. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.

How can I say that? This is solution for equation 1. So both of these x values satisfy the equation. So we'll plot it right here. So just let me multiply this out, just so we have it in mx plus b form.An educational video on absolute value graphing with an inequality.

With absolute value graphing when there's an inequality, we shade a region that makes the inequality true. Absolute Value Inequality Graphs in Two Variables. 5 videos. Concept. 3 min. Problem 1. 4 min. Problem 2. Absolute Value Inequality Graphs in Two Variables.

This property — that both the positive and the negative become positive — makes solving absolute-value equations a little tricky. But once you learn the "trick", they're not so bad. Let's start with something simple: I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases.

DO NOT try to write this as one inequality. If you try to write this solution as "–2 > x > 2", you will probably be counted wrong: if you take out the x in the middle, The first thing to do is clear the absolute value bars by splitting the inequality into two.

Then I'll solve the two linear inequalities. | 2x – 3. Thank you for watching the video. Radicals and Absolute Values - Concept. Carl Horowitz. Carl Horowitz. University of Michigan Runs his own tutoring company third. x to the third is 3 x's so this actually equal to x but because we're dealing with an odd root the cube root we do not need an absolute value because we can actually get.

Supposing you have a list of data which contains both positive numbers and negatives, and now you want to sum their absolute values which means all the negatives will be calculated as positives.

For example, you want 10+() would be 20 instead of 0. Graphing absolute value equations and inequalities is a more complex procedure than graphing regular equations because you have to simultaneously show the positive and negative solutions.

Simplify the process by splitting the equation or inequality into two separate solutions before graphing.

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