The top of a table has dimensions 2ft

Question

by (x + 3) ft
and has an area of 8ft squared
.

Which of the following equations can be used to find the value of x
for this situation?

Responses
A
2 x plus 3 is equal to 8
B
2 times open paren x plus 3 close paren is equal to 8
C
2 x plus 5 is equal to 8
D
2 times open paren 2 x plus 3 close paren is equal to 8
Question 2
PART B
Solve the equation for
.

Responses
A
0 point 5
B
2 point 5
C
1
D
1 point 5
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Answer 1

To solve the problem, we first need to determine the correct equation representing the area of the table. The area of a rectangle is calculated using the formula:

\[ \text{Area} = \text{length} \times \text{width} \]

In this case, the dimensions of the table are given as 2 ft (length) and \( (x + 3) \) ft (width), and we know that the area is 8 ft².

Thus, we can set up the equation:

\[ 2 \times (x + 3) = 8 \]

Now, let's identify this with the provided responses:

• A: \( 2x + 3 = 8 \) - This is incorrect.
• B: \( 2 \times (x + 3) = 8 \) - This is correct.
• C: \( 2x + 5 = 8 \) - This is incorrect.
• D: \( 2 \times (2x + 3) = 8 \) - This is incorrect.

So, the correct equation to use is B: \( 2 \times (x + 3) = 8 \).

Part B: Solve the equation for \( x \)

Now, let’s solve the equation \( 2(x + 3) = 8 \):

1. Divide both sides by 2: \[ x + 3 = 4 \]

2. Subtract 3 from both sides: \[ x = 4 - 3 \] \[ x = 1 \]

Thus, the value of \( x \) is 1.

So the response to Part B is C: 1.