Let's solve the expression [tex]\( |5| \times |x + 2| \)[/tex] under the condition that [tex]\( x < -3 \)[/tex].
First, let's break it down step-by-step:
1. Calculate the absolute value of 5, [tex]\( |5| \)[/tex]:
[tex]\[
|5| = 5
\][/tex]
2. Determine a specific value for [tex]\( x \)[/tex] that satisfies the condition [tex]\( x < -3 \)[/tex]:
Since there are many values that fit this condition, let's choose [tex]\( x = -4 \)[/tex] (since it is safely less than -3).
3. Calculate [tex]\( x + 2 \)[/tex] using the chosen value of [tex]\( x = -4 \)[/tex]:
[tex]\[
x + 2 = -4 + 2 = -2
\][/tex]
4. Calculate the absolute value of [tex]\( x + 2 \)[/tex], i.e., [tex]\( |-2| \)[/tex]:
[tex]\[
|-2| = 2
\][/tex]
5. Multiply the results from steps 1 and 4:
[tex]\[
|5| \times |x + 2| = 5 \times 2 = 10
\][/tex]
So, the step-by-step solution to [tex]\( |5| \times |x + 2| \)[/tex] under the condition [tex]\( x < -3 \)[/tex] is:
[tex]\[
5 \times 2 = 10
\][/tex]
Thus, the result is [tex]\( 10 \)[/tex].
