To solve the inequality \(-3x - 7 < 20\) and determine which graph represents its solution, follow these steps:
1. Isolate the term involving \(x\):
[tex]\[
-3x - 7 < 20
\][/tex]
Add 7 to both sides of the inequality to eliminate the constant term on the left side:
[tex]\[
-3x - 7 + 7 < 20 + 7
\][/tex]
Simplifying this, we get:
[tex]\[
-3x < 27
\][/tex]
2. Solve for \(x\):
Divide both sides of the inequality by \(-3\). When dividing by a negative number, we must reverse the inequality sign:
[tex]\[
\frac{-3x}{-3} > \frac{27}{-3}
\][/tex]
Simplifying this, we find:
[tex]\[
x > -9
\][/tex]
So the solution to the inequality \(-3x - 7 < 20\) is \(x > -9\).
To represent this on a graph:
- Draw a number line.
- Locate the point \(-9\) on the number line.
- Since \(x > -9\), use an open circle at \(-9\) to indicate that \(-9\) is not included in the solution.
- Shade the number line to the right of \(-9\) to indicate all numbers greater than \(-9\).
The correct graph will show a number line with an open circle at [tex]\(-9\)[/tex] and shading extending to the right.
