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.
a. the solution set is (type your answer using interval notation.)
b. the solution set is ∅
choose the correct graph below
a.
-10 -8 -6 -4 -2 0 2 4 6 8 10
b.
-10 -8 -6 -4 -2 0 2 4 6 8 10
c.
-10 -8 -6 -4 -2 0 2 4 6 8 10
d. the solution set is ∅.

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( x \), we subtract 4 from both sides of the inequality \( 2x + 4>10 \). This gives us \( 2x+4 - 4>10 - 4 \), which simplifies to \( 2x>6 \).

Step2: Divide both sides by 2

To solve for \( x \), we divide both sides of the inequality \( 2x>6 \) by 2. So, \( \frac{2x}{2}>\frac{6}{2} \), which simplifies to \( x > 3 \).
In interval notation, the solution set for \( x>3 \) is \( (3, \infty) \).

For the graph, since \( x > 3 \), we use an open circle at 3 (because 3 is not included in the solution set) and shade to the right. Looking at the options, option B has an open circle at 3 and shading to the right.

Answer:

The solution set in interval notation is \( (3, \infty) \). The correct graph is B.