To evaluate the expression \(5\left|x^3 - 2\right| + 7\) when \(x = -2\), follow these steps:
1. Substitute \(x\) into the expression \(x^3 - 2\):
[tex]\[
(-2)^3 - 2
\][/tex]
2. Calculate \((-2)^3\):
[tex]\[
(-2)^3 = -8
\][/tex]
3. Subtract 2 from -8:
[tex]\[
-8 - 2 = -10
\][/tex]
So, the value inside the absolute value is -10.
4. Find the absolute value of -10:
[tex]\[
\left|-10\right| = 10
\][/tex]
5. Substitute the absolute value back into the expression \(5\left|x^3 - 2\right| + 7\):
[tex]\[
5 \times 10 + 7
\][/tex]
6. Multiply 5 by 10:
[tex]\[
5 \times 10 = 50
\][/tex]
7. Add 7 to the result:
[tex]\[
50 + 7 = 57
\][/tex]
Thus, the value of the expression [tex]\(5\left|x^3 - 2\right| + 7\)[/tex] when [tex]\(x = -2\)[/tex] is [tex]\(\boxed{57}\)[/tex].
