Question

Translate the English phrase into an algebraic expression:
(a) The difference of two times x and 8.
(b) Two time the difference of x and 8.

Short answer

$$\begin{gathered} a)2x-8 \\ b)2(x-8) \end{gathered}$$

Step-by-step solution

Using concept:

• The expression "$a-b$" is being used to accomplish a subtraction operation, whereas the phrase "difference of a and b" has been used to perform this operation.
• The expression "$ab$" is being used to conduct a multiplication, while the phrase for this operation is a time b.

Part (a) step 1.  Write Algebraic expression of the difference of two times x and 8.

In multiplication and subtraction, there are two operation words: "times" and "difference."
Since differences in the important word, the two will be removed.
We'll subtract 8 even though we're multiplying 2 times x.
As a result, we start with multiplication.
The terms "of" and "and" in the phrase must now be highlighted. Therefore, "the difference of two times x and 8" is "$2x-8$".

Part (b) step 2.  Write Algebraic expression of two times the difference of x and 8.

In multiplication and subtraction, there really are two operation words: "times" and "difference."
Since already said, the keyword is the difference, hence the two terms would be subtracted.
They need parenthesis around "the difference of xand 2 $(x-2)$" since we're multiplying the difference by two.
As a result, the difference is established first.
The words "of" and "and" in the statement should now be highlighted. Therefore, "two times the difference of x and 8" is "$2(x-8)$".