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Choose the correct description of the graph of the compound inequality:
[tex] 3x + 2 \ \textgreater \ 5 \text{ and } 3x \leq 9 [/tex]

A. A number line with an open circle on 1, shading to the left, and a closed circle on 3, shading to the right

B. A number line with a closed circle on 1, shading to the left, and an open circle on 3, shading to the right

C. A number line with a closed circle on 1, an open circle on 3, and shading in between

D. A number line with an open circle on 1, a closed circle on 3, and shading in between



Answer :

GinnyAnswer
To solve the given compound inequality, we need to deal with both inequalities separately and then combine the results.

1. First inequality: [tex]\( 3x + 2 > 5 \)[/tex]

- Subtract 2 from both sides:
[tex]\[ 3x + 2 - 2 > 5 - 2 \implies 3x > 3 \][/tex]
- Divide both sides by 3:
[tex]\[ \frac{3x}{3} > \frac{3}{3} \implies x > 1 \][/tex]

2. Second inequality: [tex]\( 3x \leq 9 \)[/tex]

- Divide both sides by 3:
[tex]\[ \frac{3x}{3} \leq \frac{9}{3} \implies x \leq 3 \][/tex]

3. Combining the inequalities:
[tex]\[ 1 < x \leq 3 \][/tex]

This means that [tex]\( x \)[/tex] must be greater than 1 but less than or equal to 3.

4. Graphing this inequality on a number line:

- An open circle on 1, indicating that 1 is not included in the solution set.
- A closed circle on 3, indicating that 3 is included in the solution set.
- Shading in between, covering all values between 1 and 3.

So, the correct description of the graph of the compound inequality is:

A number line with an open circle on 1, a closed circle on 3, and shading in between.

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