Let's carefully analyze and solve the problem step-by-step.
1. Understand the Problem:
- You have a piece of string and the length of this string is denoted by [tex]\( x \)[/tex] centimeters (cm).
- You then cut off 8 cm from this piece of string.
- You need to find the length of the remaining piece of string.
2. Initial Length:
- The initial length of the string is [tex]\( x \)[/tex] cm.
3. Cutting Off a Piece:
- You are cutting off 8 cm from this piece of string. This means you are removing 8 cm from the total length [tex]\( x \)[/tex].
4. Calculate the Remaining Length:
- The remaining length of the string after cutting off 8 cm would be the original length [tex]\( x \)[/tex] minus the 8 cm that was cut off.
- This can be expressed mathematically as:
[tex]\[
\text{Remaining Length} = x - 8 \text{ cm}
\][/tex]
5. Identify the Correct Option:
- The remaining length of the string is expressed as [tex]\( x - 8 \)[/tex] cm.
- Among the given options:
- Option (a) is [tex]\( x + 8 \)[/tex], which implies the length would increase, which is not correct.
- Option (b) is [tex]\( 8x \)[/tex], which implies multiplying the length by 8, which is not relevant here.
- Option (c) is [tex]\( \frac{x}{8} \)[/tex], which implies dividing the length by 8, again not related to subtracting 8 cm.
- Option (d) is [tex]\( x - 8 \)[/tex], which correctly represents subtracting 8 cm from the original length.
Hence, the correct answer is:
[tex]\[ \boxed{d \; x - 8} \][/tex]
