Look at the inequality below.

Question

3n+7<4
Which graph represents the solution to the inequality shown?

A.

A number line between -1 and 3 has a bold line start with a closed circle between 2 and 3 and heads rightwards.

B.

A number line between -1 and 3 has a bold line start with a closed circle between 2 and 3 and heads leftwards.

C.

A number line between -1 and 3 has a bold line start with a closed circle at -1 and heads rightwards.

D.

A number line between -1 and 3 has a bold line start with a closed circle at -1 and heads leftwards.

Answer 1

To solve the inequality \( 3n + 7 < 4 \), we can start by isolating \( n \):

1. Subtract 7 from both sides: \[ 3n < 4 - 7 \] \[ 3n < -3 \]

2. Now, divide both sides by 3: \[ n < -1 \]

The solution to the inequality is \( n < -1 \). This means that we want all values of \( n \) that are less than -1 on a number line, with an open circle at -1, indicating that -1 itself is not included in the solution.

Now, we need to look at the graph options provided:

A. A bold line starting with a closed circle between 2 and 3 and heads rightwards — not correct. B. A bold line starting with a closed circle between 2 and 3 and heads leftwards — not correct. C. A bold line starting with a closed circle at -1 and heads rightwards — not correct. D. A bold line starting with a closed circle at -1 and heads leftwards — correct.

The correct answer is D.