# Absolute Value (algebraic version)....1

• nycmathguy
In summary, Absolute Value (algebraic version) is a rule that states that when x is greater than or equal to 0, the absolute value of x is equal to x. When x is less than 0, the absolute value of x is equal to -x. This can be rewritten as -(x - 3) = -x + 3.
nycmathguy
Homework Statement
Rewrite each expression without using absolute value notation.
Relevant Equations
n/a
Absolute Value (algebraic version)
Rule:

| x | = x when x ≥ 0

| x | = -x when x > 0

Rewrite each expression without using absolute value notation.

Question 1

|1 - sqrt{2} | + 1

The value 1 - sqrt{2} = a negative value.

So, -(1 - sqrt{2}) = - 1 + sqrt{2}.

When I put it all together, I get this:

-1 + sqrt{2} + 1

You say?

Question 2

| x - 3 | given that x < 3.

If x < 3, then x - 3 is a negative value.

So, -(x - 3) becomes -x + 3.

You say?

I agree also for this.
Ssnow

Ssnow said:
I agree also for this.
Ssnow
I got it right again. Not bad for a person that has been attacked since joining the site for trying to learn precalculus, a subject that IS WAY OVER MY HEAD.

symbolipoint

## 1. What is absolute value?

Absolute value is a mathematical concept that represents the distance of a number from zero on a number line. It is always a positive value, regardless of the sign of the number.

## 2. How is absolute value expressed algebraically?

The algebraic expression for absolute value is |x|, where x is the number being evaluated. This means that the absolute value of x is equal to the positive value of x, regardless of its original sign.

## 3. What is the difference between absolute value and regular value?

The main difference between absolute value and regular value is that absolute value is always positive, while regular value can be positive, negative, or zero. Absolute value also represents the distance from zero, while regular value represents the actual value of a number.

## 4. How do you solve equations involving absolute value?

To solve equations involving absolute value, you must consider both the positive and negative solutions. This means setting up two separate equations, one with the positive value of x and one with the negative value of x, and solving for each separately.

## 5. Can absolute value be applied to complex numbers?

Yes, absolute value can be applied to complex numbers. In this case, the absolute value represents the distance of the complex number from the origin on the complex plane.

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