To determine which statement correctly describes the expression [tex]\(\left|x^3\right| + 5\)[/tex], let's evaluate each option step by step:
Option A: The sum of the absolute value of three times a number and 5.
- This statement suggests the expression [tex]\(\left|3x\right| + 5\)[/tex].
- [tex]\(\left|3x\right|\)[/tex] means taking the absolute value after multiplying a number [tex]\(x\)[/tex] by 3.
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option A is incorrect.
Option B: 5 more than the absolute value of the cube of a number.
- This statement suggests the operation of cubing a number [tex]\(x\)[/tex], taking the absolute value of the result, and then adding 5.
- Mathematically, this is written as [tex]\(\left|x^3\right| + 5\)[/tex].
- This matches the given expression exactly, so option B is correct.
Option C: The absolute value of three times a number added to 5.
- This statement also suggests the expression [tex]\(\left|3x\right| + 5\)[/tex].
- Similar to Option A, this involves taking the absolute value after multiplying [tex]\(x\)[/tex] by 3 and then adding 5.
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option C is incorrect.
Option D: The cube of the sum of a number and 5.
- This statement suggests adding a number [tex]\(x\)[/tex] to 5 first and then cubing the result.
- Mathematically, this is written as [tex]\((x + 5)^3\)[/tex].
- This is not the same as [tex]\(\left|x^3\right| + 5\)[/tex], so option D is incorrect.
Therefore, the statement that correctly describes the expression [tex]\(\left|x^3\right| + 5\)[/tex] is option B: 5 more than the absolute value of the cube of a number.
