# Understanding Negative Numbers in -2x |X| < 4 Equation

• brycenrg
In summary: Thanks for the reply, but aren't you graphing -2*|x| for the interval -4 ≤ x ≤ 4?For example f(-3) = -6 because -2 *|-3| = -6?thats why I am thinking the graph at -4 ≤ x ≤ 0 should be negative numbers not positiveNo, -2*|x| is the same as -2|x| when x is in the range -4 ≤ x ≤ 4.
brycenrg

## Homework Statement

This is the solution, the question was find its domain.

## Homework Equations

How does |X| (less than or equal to) 4, when a negative number is inputed into -2x how does that = a positive number?

## The Attempt at a Solution

On the graph to me All X values < 0 should be negative or atleast until -5
Because the -2x if |x| < 4

If we put f(2) -2 * |2| = -4 which works on the graph but if I put -2 which would equal positive 2 because of the absolute value the graph seems to not make sense for me.
f(-2) should equal -4 as well right?

brycenrg said:

## Homework Statement

View attachment 67376
This is the solution, the question was find its domain.

## Homework Equations

How does |X| (less than or equal to) 4, when a negative number is inputed into -2x how does that = a positive number?

f(-2) = -2(-2) = + 4
f(3) = -2(3) = -6

## The Attempt at a Solution

On the graph to me All X values < 0 should be negative or atleast until -5
I think that you are confusing values in the domain with the resulting function values.

The function has three different formulas, with each valid on a different interval. For input values between -4 and 4, the middle formula is used.
brycenrg said:
Because the -2x if |x| < 4

If we put f(2) -2 * |2| = -4 which works on the graph but if I put -2 which would equal positive 2 because of the absolute value the graph seems to not make sense for me.
f(-2) should equal -4 as well right?
You are not graphing y = |x|, which seems to be part of your confusion here. They could just as well have said that the middle formula applies if -4 ≤ x ≤ 4.

Thanks for the reply, but aren't you graphing -2*|x| for the interval -4 ≤ x ≤ 4?
For example f(-3) = -6 because -2 *|-3| = -6?
thats why I am thinking the graph at -4 ≤ x ≤ 0 should be negative numbers not positive

brycenrg said:
Thanks for the reply, but aren't you graphing -2*|x| for the interval -4 ≤ x ≤ 4?
For example f(-3) = -6 because -2 *|-3| = -6?
thats why I am thinking the graph at -4 ≤ x ≤ 0 should be negative numbers not positive

No. The problem says for |x|<=4, f(x)=-2x. That's not the same as saying for |x|<=4, f(x)=-2|x|.

I see I am confused. I thought the right side |x| <= 4 means any value less than or equal to 4 but because its x is in absolute value brackets if x was -1 it would be 1 so then you would plug 1 into -2x? What is the point of the |x| then? Does that make sense on my confusion lol?

brycenrg said:
I see I am confused. I thought the right side |x| <= 4 means any value less than or equal to 4
That's not what |x| ≤ 4 means. -5 ≤ 4, but -5 doesn't satisfy |x| ≤ 4.
brycenrg said:
but because its x is in absolute value brackets if x was -1 it would be 1 so then you would plug 1 into -2x?
NO.
brycenrg said:
What is the point of the |x| then?
The ONLY purpose of the absolute value here is to define the interval on which the second formula should be applied.

The second part of the function's definition could have been written as
f(x) = -2x, if -4 ≤ x -4

To answer your question above, f(-1) = -2(-1) = +2.
brycenrg said:
Does that make sense on my confusion lol?

Always think! What numbers can I put in for x so |x| is less than 4. I like to think and teach that the absolute of any number is that same exact number but without a sign. So in |x|<4 we are asking which number or numbers, if any, when we ignore the sign will be less than 4. I will give you a hint, there are 7 integers in this set.

## 1. What is the meaning of a negative number in the equation -2x |X| < 4?

A negative number in this equation represents a value that is less than zero. It indicates a direction or quantity that is opposite of what is considered positive. In the context of this equation, it is used to represent the values of x that will satisfy the inequality.

## 2. How do you solve for x in the equation -2x |X| < 4?

To solve for x in this equation, you first need to isolate the absolute value by dividing both sides by -2. This will result in two inequalities: x > -2 and x < 2. Since these two inequalities need to be satisfied simultaneously, the solution set for x is -2 < x < 2.

## 3. Can the absolute value in the equation -2x |X| < 4 be removed?

No, the absolute value cannot be removed as it is an important part of the equation. It is used to ensure that both sides of the inequality are positive, which is necessary for solving the equation.

## 4. How are negative numbers used in real-life scenarios?

Negative numbers are used in real-life scenarios to represent situations where a decrease or loss is occurring. For example, a negative number may represent a decrease in temperature, a loss of money, or a decrease in elevation.

## 5. Why is it important to understand negative numbers in equations?

Understanding negative numbers in equations is important because it allows us to accurately represent and solve real-life problems. Negative numbers are also used in advanced mathematical concepts, such as calculus and physics, so having a solid understanding of them is crucial for success in these fields.

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