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Question 15 (5 points)

Evaluate the expression [tex]|2x - 5|[/tex] for [tex]x = -3[/tex] and for [tex]x = 3[/tex].

A) 3, 13

B) 1, 11

C) 13, 3

D) 11, 1

Sagot :

GinnyAnsweridn
To evaluate the expression [tex]\( |2x - 5| \)[/tex] for [tex]\( x = -3 \)[/tex] and [tex]\( x = 3 \)[/tex], let's proceed step-by-step.

### Case 1: [tex]\( x = -3 \)[/tex]

1. Substitute [tex]\( x = -3 \)[/tex] into the expression:
[tex]\[ |2(-3) - 5| \][/tex]

2. Simplify inside the absolute value:
[tex]\[ 2 \cdot (-3) = -6 \][/tex]
[tex]\[ -6 - 5 = -11 \][/tex]

3. Apply the absolute value:
[tex]\[ |-11| = 11 \][/tex]

So, for [tex]\( x = -3 \)[/tex], the value is 11.

### Case 2: [tex]\( x = 3 \)[/tex]

1. Substitute [tex]\( x = 3 \)[/tex] into the expression:
[tex]\[ |2(3) - 5| \][/tex]

2. Simplify inside the absolute value:
[tex]\[ 2 \cdot 3 = 6 \][/tex]
[tex]\[ 6 - 5 = 1 \][/tex]

3. Apply the absolute value:
[tex]\[ |1| = 1 \][/tex]

So, for [tex]\( x = 3 \)[/tex], the value is 1.

### Summary

The values of the expression [tex]\( |2x - 5| \)[/tex] for [tex]\( x = -3 \)[/tex] and [tex]\( x = 3 \)[/tex] are:
[tex]\[ 11 \text{ and } 1 \][/tex]

Hence, the correct answer is:
D) 11, 1
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