Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which graph shows the solution set for [tex]2x + 3 \ \textgreater \ -9[/tex]?

Sagot :

GinnyAnswer
To determine the solution set for the inequality [tex]\(2x + 3 > -9\)[/tex], let's go through the steps:

1. Start with the original inequality:
[tex]\[ 2x + 3 > -9 \][/tex]

2. Isolate the term with [tex]\(x\)[/tex] by subtracting 3 from both sides of the inequality:
[tex]\[ 2x + 3 - 3 > -9 - 3 \][/tex]
[tex]\[ 2x > -12 \][/tex]

3. Solve for [tex]\(x\)[/tex] by dividing both sides of the inequality by 2:
[tex]\[ \frac{2x}{2} > \frac{-12}{2} \][/tex]
[tex]\[ x > -6 \][/tex]

Thus, the solution to the inequality is [tex]\( x > -6 \)[/tex].

### Graphing the Solution Set

To graph the solution [tex]\( x > -6 \)[/tex]:

1. Draw a number line.
2. Locate the point [tex]\( -6 \)[/tex] on the number line.
3. Since the inequality is strictly greater than ( [tex]\( > \)[/tex] ), we use an open circle at [tex]\( -6 \)[/tex] to indicate that [tex]\(-6\)[/tex] is not included in the solution.
4. Shade the number line to the right of [tex]\( -6 \)[/tex] to indicate all numbers greater than [tex]\(-6\)[/tex].

The graph represents all values of [tex]\(x\)[/tex] that satisfy the inequality [tex]\(2x + 3 > -9\)[/tex].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.