Use the image to answer the question.

Question

there is a line from -10 to positive 10, there is a dot on the number positive 1.75.
Nora solved an inequality and graphed the solution on the number line.
Which of the following inequalities did she solve?
A. 8x > 14
B. 1.75x < 3.5
C. 4x > 7
D. 6x < 10.5

Answer 1

To determine which inequality Nora solved, let's first identify the potential value for \( x \) based on the number line. The dot at \( x = 1.75 \) must satisfy the inequality.

Let's evaluate each inequality option by substituting \( x = 1.75 \):

A. \( 8x > 14 \)
\[ 8(1.75) = 14 \]
Which results in:
\[ 14 > 14 \]
This is not true, so A is incorrect.

B. \( 1.75x < 3.5 \)
\[ 1.75(1.75) = 3.0625 \]
Which results in:
\[ 3.0625 < 3.5 \]
This is true, so B is a valid option.

C. \( 4x > 7 \)
\[ 4(1.75) = 7 \]
Which results in:
\[ 7 > 7 \]
This is not true, so C is incorrect.

D. \( 6x < 10.5 \)
\[ 6(1.75) = 10.5 \]
Which results in:
\[ 10.5 < 10.5 \]
This is not true either, so D is incorrect.

Therefore, the inequality Nora solved is:
\[ \boxed{1.75x < 3.5} \]

Answer 2

just choose one that is close to the correct answer

Answer 3

Given your request to choose one that is close to the correct answer, let's consider the inequalities without strictly evaluating exact equality. We'll look for the one that makes logical sense given \(x = 1.75\).

A. \(8x > 14\)
\[8(1.75) = 14\]
Exactly 14, suggesting not greater than, so not correct but close.

B. \(1.75x < 3.5\)
\[1.75(1.75) = 3.0625\]
This is true.

C. \(4x > 7\)
\[4(1.75) = 7\]
Exactly 7, suggesting not greater than, so not correct but also close.

D. \(6x < 10.5\)
\[6(1.75) = 10.5\]
Exactly 10.5, suggesting not less than, so not correct but close.

B is precisely correct, but given the condition to choose one close rather than exact, the closest logical inequality would still be:
\[ B. \boxed{1.75x < 3.5} \]