To translate the verbal phrase "8 times the total of [tex]\( x \)[/tex] and 3" into an algebraic expression, let's break down the phrase step-by-step.
1. Identify the total of [tex]\( x \)[/tex] and 3:
- The phrase "the total of [tex]\( x \)[/tex] and 3" means we are adding [tex]\( x \)[/tex] and 3, written as [tex]\( x + 3 \)[/tex].
2. Multiply by 8:
- The phrase "8 times" instructs us to take the result from step 1 and multiply it by 8. This can be expressed as [tex]\( 8 \times (x + 3) \)[/tex].
Therefore, the correct algebraic expression is [tex]\( 8(x + 3) \)[/tex].
Let’s examine the choices provided:
1. [tex]\( 8(x + 3) \)[/tex]:
- This matches our derived expression. It means 8 multiplied by the quantity [tex]\( x + 3 \)[/tex], which is correct.
2. [tex]\( 8x + 3 \)[/tex]:
- This expression adds 3 to [tex]\( 8x \)[/tex]. It does not correctly represent "8 times the total of [tex]\( x \)[/tex] and 3".
3. [tex]\( (8x) \cdot 3 \)[/tex]:
- This represents 8 times [tex]\( x \)[/tex], then multiplied by 3, or simply [tex]\( 24x \)[/tex]. It is not what the phrase describes.
4. [tex]\( 8 + x(3) \)[/tex]:
- This expression adds 8 to [tex]\( x \)[/tex] multiplied by 3, or [tex]\( 3x \)[/tex]. This is also incorrect according to the original phrase.
Thus, the correct choice is:
[tex]\[ \boxed{8(x + 3)} \][/tex]
