Question

the solution set of the inequality is 2,6. (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in interval notation.) choose the correct graph. \\(\bigcirc\\) a. \\(\longleftarrow\frac{}{}-10\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}0\frac{}{}\boldsymbol{\longleftarrow\longrightarrow}\frac{}{}\frac{}{}\frac{}{}10\longrightarrow\\) \\(\bigcirc\\) b. \\(\longleftarrow\frac{}{}-10\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}0\frac{}{}\boldsymbol{\longleftarrow\longrightarrow}\frac{}{}\frac{}{}\frac{}{}\infty\longrightarrow\\) \\(\bigcirc\\) c. \\(\longleftarrow\frac{}{}-10\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}0\frac{}{}\boldsymbol{\longleftarrow\longrightarrow}\frac{}{}\frac{}{}\frac{}{}10\longrightarrow\\) \\(\bigcirc\\) d. \\(\longleftarrow\frac{}{}-10\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\boldsymbol{\longleftarrow\longrightarrow}\frac{}{}0\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\frac{}{}\infty\longrightarrow\\)

Explanation:

Step1: Analyze the interval notation [2,6]

The interval [2,6] means all real numbers from 2 (inclusive) to 6 (inclusive). On a number line, we look for a graph that has a closed circle (or bracket) at 2 and 6, and the line segment between them.

Step2: Evaluate each option

• Option A: The interval shown starts from around 2 (but the bracket is at the end, but the start is not at 2. Wait, looking at the number line, the graph in A has a bracket at the right end around 6? No, actually, looking at the positions, the correct graph for [2,6] should have the segment between 2 and 6. Let's check the number lines:
• Option A: The blue segment starts after 0, with a bracket at the right. But the numbers: from the number line, the left end of the blue segment in A is around 2? Wait, the number line has -10, 0, 10. So 2 is between 0 and 10, 6 is also between 0 and 10. Option C: The blue segment starts at 2 (since the bracket is at 2) and ends at 6 (bracket at 6), between 0 and 10. Wait, no, let's re - examine:

Wait, the number lines:

• Option A: The blue arrow is a segment with a bracket at the right, starting from a point after 0. But the interval [2,6] should be between 2 and 6.
• Option B: It's an arrow going to the right, starting from a point after 0, which is an open interval or going to infinity, not [2,6].
• Option C: The blue segment has brackets at both ends, between 2 and 6 (since on the number line from 0 to 10, 2 and 6 are in that range). Wait, no, the number line in C: the blue segment starts at 2 (bracket) and ends at 6 (bracket), which is exactly the interval [2,6].
• Option D: The blue segment is between - 10 and 0, which is not [2,6].

Answer:

C. The graph with a blue segment between 2 and 6 (with brackets at both ends) on the number line from - 10 to 10, centered around 0.