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

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

6 0

4 years ago

Which is the simplified form of the expression? Question 10 options: 9n – 2 9n + 2 15n – 2 15n – 8

KATRIN_1 [288]

Answer:

Combine -15 + 2n first, then you get -13 n.

Then work from -13n to subtracting -9n, that is -4n. Now all you have left is -4n = 8. Divide both sides by -4n/-4 8/-4. The answer is n = -2.

Step-by-step explanation:

3 0

3 years ago

Write the expression without the fraction bar.

snow_tiger [21]

The answer is y^-1 :) when you have two exponents over a y in a fraction or divison, you always subtract the top from the bottom. hope this helps!

8 0

3 years ago