To solve the inequality [tex]\(-7x > 21\)[/tex], follow these steps:
1. Identify the inequality: [tex]\(-7x > 21\)[/tex].
2. Divide both sides of the inequality by [tex]\(-7\)[/tex] to isolate [tex]\(x\)[/tex]. Remember, when you divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.
[tex]\[
x < \frac{21}{-7}
\][/tex]
3. Perform the division:
[tex]\[
x < -3
\][/tex]
Thus, the solution to the inequality [tex]\(-7x > 21\)[/tex] is [tex]\(x < -3\)[/tex].
To graph this solution, you should:
1. Draw a number line.
2. Locate the point [tex]\( -3 \)[/tex] on this number line.
3. Since [tex]\(x\)[/tex] is less than [tex]\(-3\)[/tex], you should use an open circle at [tex]\(-3\)[/tex] to indicate that [tex]\( -3 \)[/tex] is not included in the solution set.
4. Shade the number line to the left of [tex]\(-3\)[/tex], indicating all values less than [tex]\(-3\)[/tex].
Each of the given options (A), (B), (C), and (D) involves graphical depictions. Based on the description:
- Correct option to select is the one that shows an open circle at [tex]\(-3\)[/tex] and shading to the left of [tex]\(-3\)[/tex].
Thus, the correct graph of the solution will be the one corresponding to the correct depiction described.
