Question

working with absolute value - independent practice worksheet
complete all the problems.

1. find the absolute value.

(a) |-3| = ____ (b) |-77| = ____

1. simplify each equation below.

(a) -7 - |7| = ____ (b) -|-2| + |9| = ____

1. find the absolute value.

(a) |36| = ____ (b) |-45| = ____

1. simplify each equation below.

(a) 10 - |8| = ____ (b) -|-12| + |20| = ____

1. find the absolute value.

(a) |-28| = ____ (b) |59| = ____

1. simplify each equation below.

(a) -19 - |5| = ____ (b) |-17| + |25| = ____

1. find the absolute value.

(a) |-87| = ____ (b) |-67| = ____

1. simplify each equation below:

(a) -32 - |28| = ____ (b) -|-11| + |16| = ____

1. find the absolute value.

(a) |-28| = ____ (b) |16| = ____

1. simplify each equation below.

(a) -45 - |35| = ____ (b) -|-55| + |30| = ____

Explanation:

Problem 1

(a)

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line, so \( |-a| = a \) for \( a>0 \).
For \( |-3| \), using the definition, \( |-3| = 3 \).

Step2: No further steps needed.

Step1: Apply absolute value rule

Using the rule \( |-a| = a \) for positive \( a \), for \( |-77| \), we have \( |-77| = 77 \).

Step2: No more steps.

Step1: Find absolute value of 7

First, \( |7| = 7 \) (since the absolute value of a positive number is itself).

Step2: Subtract from -7

Then, \( -7 - |7| = -7 - 7 \).

Step3: Perform subtraction

\( -7 - 7 = -14 \).

Answer:

3

(b)