Multiple Choice Question

Question

Look at the inequality below.

Which graph represents the solution to the inequality shown?
3n + 7 < 4
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 will first isolate \(n\):

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

2. Divide both sides by 3: \[ n < -1 \]

The solution to the inequality is \(n < -1\), which means we need to represent this on a number line.

Looking at the options given:

• A: A closed circle between 2 and 3 heading rightwards (incorrect).
• B: A closed circle between 2 and 3 heading leftwards (incorrect).
• C: A closed circle at -1 heading rightwards (incorrect).
• D: A closed circle at -1 heading leftwards (correct image representing \(n < -1\)).

The correct answer is D. A number line between -1 and 3 has a bold line start with a closed circle at -1 and heads leftwards.