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In $15-26,$ find and graph the solution set of each inequality.$$|2-4 b| \leq 6$$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

01:58

In $15-26,$ find and graph…

01:28

02:54

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Solve each inequality. Gra…

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In $15-26,$ solve each ine…

all right. Hey, guys. So, in this problem, we're given the inequality. Absolute value of two minus four B is less than or equal to six were asked to solve for the solution set and then graphic. So first things first, let's break apart our absolute value into the two inequalities that we need to solve. And in this case, the two inequalities that we needed to solve is to minus for B is less than or equal to six and to minus four. B is greater than or equal to minus six. So this is absurd value. Inequality breaks into two these two things. And so let's solve the one equation on the left. So first, what we're going to do is we're going to subtract two on both sides. The twos cancel out on the left side, leaving us with minus for B on the right hand side. We're left with four, and we divide out by a negative four. And when we divide up by a negative four, we get negative one on the right hand side. And when you divide out by a negative value, the quote, the inequality sign flips. So our answer to our left hand equation with this equation right here is B is greater than or equal toe one. And now let's take a look at this equation right here. So we do the same thing. We subtract two from both sides on the left hand side. The twos cancel out and you're left with minus four. B is greater than or equal to negative. Eight. You divide out our negative four on both sides, and then when you do that, you're left would be on the left hand side and you're left with B is less than are equal to two. And since, um, you're dividing by a negative number than equality flips, that's why becomes a less than or equal to. So let's graft this out really quickly at the solution set. So we have basically lets give us some values. We have negative one. Let's see, this is negative. One that's gonna be your 01 So this is our to value. So when we graft this were saying that we have our negative one point here customs. It's a greater than or equal to. We include the negative one, and since it's a less than or equal to two We include are, too as well. So when we say B is greater than or equal to negative one, and B is less than or equal to two. Ah, the graph includes the solution set right here. So basically anything in between one and two. And this is the graph of our solution set. Ah, negative B is greater than or equal to negative one, and B is less than a wrinkle to two. And another way to write this is negative. One is less than or equal to be is less than or equal to two. Just a nicer shorthand way of writing it. So this is the answer, and this is the graph of the solution set to this inequality.

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