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4 years ago

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Students in a science class are divided into 6 equal groups with at least 4 students in each group. Identify an inequality that

represents the number of students in the class. Would x/6 > or equal to 4 be correct?

1 answer:

worty [1.4K]4 years ago

7 0

Yes bc 6 groups and a bout 4 are in it ...........

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Solve the equation and show all work. 4|x + 1/3| = 20 <br> i'm kind of stuck hhh

34kurt

Absolute value is a function that takes some number and outputs the size of that number, regardless of the sign. By definition, $|x|=x$ if $x\ge0$ , and $|x|=-x$ if $x$ .

For example,

|2| = 2 because the input 2 is positive, so the input is unchanged;
|-3| = -(-3) = 3 because the input -3 is negative, so the sign is switched.

What this means for this problem is that there are two cases to consider:

If $x+\frac13\ge0$ , then $\left|x+\frac13\right|=x+\frac13$ , so that

$4\left(x+\dfrac13\right)=20\implies x+\dfrac13=5\implies\boxed{x=\dfrac{14}3}$

On the other hand, if $x+\frac13$ , then $\left|x+\frac13\right|=-\left(x+\frac13\right)$ , so

$-4\left(x+\dfrac13\right)=20\implies x+\dfrac13=-5\implies\boxed{x=-\dfrac{16}3}$

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