Let's solve the inequality step-by-step:
Given inequality:
[tex]\[ -3x - 7 < 20 \][/tex]
1. Add 7 to both sides:
[tex]\[ -3x - 7 + 7 < 20 + 7 \][/tex]
[tex]\[ -3x < 27 \][/tex]
2. Divide both sides by -3:
Remember, when you divide or multiply both sides of an inequality by a negative number, you have to reverse the direction of the inequality.
[tex]\[ x > \frac{27}{-3} \][/tex]
[tex]\[ x > -9 \][/tex]
Thus, the solution to the inequality [tex]\( -3x - 7 < 20 \)[/tex] is [tex]\( x > -9 \)[/tex].
### Graphing the Inequality:
To graph this inequality:
- Number line: You can use a horizontal number line.
- Point: Identify the point [tex]\( -9 \)[/tex].
- Open circle: Place an open circle on [tex]\(-9\)[/tex] to indicate that [tex]\(-9\)[/tex] is not included in the solution.
- Shaded region: Shade the number line to the right of [tex]\(-9\)[/tex], indicating all numbers greater than [tex]\(-9\)[/tex].
The graph looks as follows:
[tex]\[ \xrightarrow{\ \ \ \ \ \ \ \ \ \ \ -9 \ \ \ \rightarrow} \][/tex]
Where the open circle at [tex]\( -9 \)[/tex] and the shaded region to the right illustrate [tex]\( x > -9 \)[/tex].
