Question

other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
\\(2x + 4 > 10\\)

select the correct choice below and, if necessary, fill in the answer box to complete your choice
\\(\bigcirc\\) a. the solution set is \\(\square\\) (type your answer using interval notation.)
\\(\bigcirc\\) b. the solution set is \\(\varnothing\\).

choose the correct graph below.
\\(\bigcirc\\) a.
\\(\leftarrow\\) \\(-10\\) \\(-8\\) \\(-6\\) \\(-4\\) \\(-2\\) \\(0\\) \\(2\\) \\(\boldsymbol{\bigg}\\) \\(4\\) \\(6\\) \\(8\\) \\(10\\) \\(\
ightarrow\\)
\\(\bigcirc\\) b.
\\(\leftarrow\\) \\(-10\\) \\(-8\\) \\(-6\\) \\(-4\\) \\(-2\\) \\(0\\) \\(2\\) \\(\boldsymbol{\bigg(}\\) \\(4\\) \\(6\\) \\(8\\) \\(10\\) \\(\
ightarrow\\)
\\(\bigcirc\\) c.
\\(\leftarrow\\) \\(-10\\) \\(-8\\) \\(-6\\) \\(-4\\) \\(-2\\) \\(0\\) \\(2\\) \\(\boldsymbol{\bigg)}\\) \\(4\\) \\(6\\) \\(8\\) \\(10\\) \\(\
ightarrow\\)
\\(\bigcirc\\) d. the solution set is \\(\varnothing\\)

Explanation:

Step1: Isolate the variable term

Subtract 4 from both sides:
$2x + 4 - 4 > 10 - 4$
$2x > 6$

Step2: Solve for x

Divide both sides by 2:
$\frac{2x}{2} > \frac{6}{2}$
$x > 3$

Step3: Write in interval notation

All values greater than 3 correspond to the interval $(3, \infty)$

Step4: Match to the number line

An open circle at 3 and arrow pointing right matches option B.

Answer:

For the solution set choice: A. The solution set is $(3, \infty)$
For the graph choice: B. <the number line with open circle at 3 and arrow pointing right>