Question

Two times a number x increased by 8 is 20. Which one of the following equations represents this statement?
8x + 2 = 20
2(4x + 2) = 20
2(x + 4) = 20
8x - 2 = 20

Answer 1

To translate the statement "Two times a number \( x \) increased by 8 is 20" into an equation, we follow these steps:

1. Identify "two times a number \( x \)": This can be expressed as \( 2x \).
2. Identify "increased by 8": This means we add 8 to the previous expression, resulting in \( 2x + 8 \).
3. The complete statement now reads: "Two times a number \( x \) increased by 8 is 20," which translates to the equation:

\[
2x + 8 = 20
\]

Now, let's look at the options provided:

1. \( 8x + 2 = 20 \)
2. \( 2(4x + 2) = 20 \)
3. \( 2(x + 4) = 20 \)
4. \( 8x - 2 = 20 \)

None of these options directly match \( 2x + 8 = 20 \).

However, if we examine option 3, \( 2(x + 4) = 20 \):
- \( 2(x + 4) = 20 \) can be expanded as \( 2x + 8 = 20 \).

Thus, the correct equation that represents the statement is:

**Option 3: \( 2(x + 4) = 20 \)**.