Question

the solution set to $6 + 2n > 12$ is $n > 3$. which are correct representations of this solution? select two options.
${n | n < 3}$
${n | n \geq 3}$
number line with open circle at 3 and arrow to the right
number line with open circle at 3 and arrow to the left
$(3, \infty)$

Explanation:

Step1: Analyze set-builder notation

Check each set-builder option against $n>3$:

• $\{n \mid n < 3\}$: Represents values less than 3, incorrect.
• $\{n \mid n \geq 3\}$: Represents values greater than or equal to 3, incorrect.

Step2: Analyze number lines

Check each number line against $n>3$:

• First number line: Open circle at 3, arrow right (values >3), correct.
• Second number line: Open circle at 3, arrow left (values <3), incorrect.

Step3: Analyze interval notation

Check $(3, \infty)$: This notation represents all real numbers greater than 3, which matches $n>3$, correct.

Answer:

• $\boldsymbol{\longleftarrow\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\circ\!\!\!\!\!\!\!\!\!\!\!

ightarrow}_{\scriptsize{-5\!\!\!\!-4\!\!\!\!-3\!\!\!\!-2\!\!\!\!-1\!\!\!\!0\!\!\!\!1\!\!\!\!2\!\!\!\!3\!\!\!\!4\!\!\!\!5}}$

• $\boldsymbol{(3, \infty)}$