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].
