Exercise 115 Page 433

Practice makes perfect

Let's begin by recalling the definition of the absolute value of a number.

Absolute Value of a Number
The distance between the number and 0 on a number line

In other words, the absolute value of a number is the non-negative value of that number. The absolute value of a number a can be written as |a|. If a is a non-negative number, then the following properties hold. |a| = a and |- a| = a We want to simplify the given absolute value expression. Let's start by calculating the expression inside the absolute value.

|5-6+1|

SubTerm

Subtract term

|- 1+1|

AddTerms

Add terms

|0|

AbsPos

|0|=0

We are asked to simplify the given expression. - 2 |- 16| Let's simplify the expression using the fact that the absolute value of a number is the non-negative value of that number.

- 2 |- 16|

AbsNeg

|-16|=16

- 2* 16

Multiply

- 32

Let's consider the given expression. |6-2|+|- 8-1| We want to simplify the expression. We can start by calculating the expressions inside the absolute values.

|6-2|+|- 8-1|

SubTerms

Subtract terms

|4|+|- 9|

AbsPos

|4|=4

4+|- 9|

AbsNeg

|-9|=9

4+9

AddTerms

Add terms