Let's evaluate each absolute value expression step-by-step.
a. [tex]\( |54| \)[/tex]
The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore:
[tex]\[ |54| = 54 \][/tex]
b. [tex]\( -\left|-7 \frac{3}{5}\right| \)[/tex]
First, convert the mixed number to an improper fraction:
[tex]\[ -7 \frac{3}{5} = -\left(7 + \frac{3}{5}\right) = -\left(\frac{35}{5} + \frac{3}{5}\right) = -\left(\frac{38}{5}\right) \][/tex]
Next, evaluate the absolute value:
[tex]\[ \left| -\frac{38}{5} \right| = \frac{38}{5} \][/tex]
Since the expression is negative of the absolute value:
[tex]\[ -\left|\frac{38}{5}\right| = -\frac{38}{5} = -7.6 \][/tex]
c. [tex]\( |3| - |-1| \)[/tex]
Evaluate the absolute values separately:
[tex]\[ |3| = 3 \][/tex]
[tex]\[ |-1| = 1 \][/tex]
Subtract the absolute values:
[tex]\[ 3 - 1 = 2 \][/tex]
d. [tex]\( |2.2 - 5.13| \)[/tex]
Evaluate the expression inside the absolute value:
[tex]\[ 2.2 - 5.13 = -2.93 \][/tex]
Now, find the absolute value:
[tex]\[ |-2.93| = 2.93 \][/tex]
So, the evaluated absolute value expressions are:
a. [tex]\( 54 \)[/tex]
b. [tex]\( -7.6 \)[/tex]
c. [tex]\( 2 \)[/tex]
d. [tex]\( 2.93 \)[/tex]
