- #1

#### 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

Answer: sqrt{2}

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?

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

Answer: sqrt{2}

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?