To solve the inequality [tex]\(-7x < -21\)[/tex], follow these steps:
1. Identify the given inequality:
We start with [tex]\(-7x < -21\)[/tex].
2. Isolate the variable [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to divide both sides of the inequality by [tex]\(-7\)[/tex]. However, remember that when dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign will reverse.
[tex]\[ -7x < -21 \][/tex]
Dividing both sides by [tex]\(-7\)[/tex]:
[tex]\[ x > \frac{-21}{-7} \][/tex]
[tex]\[ x > 3 \][/tex]
3. Interpret the result:
The solution to the inequality is [tex]\( x > 3 \)[/tex].
4. Choose the correct solution set from the given options:
- [tex]\((x \mid x < 3)\)[/tex]
- [tex]\((x \mid x > 3)\)[/tex]
- [tex]\((x \mid x < -3)\)[/tex]
- [tex]\(\{x \mid x > -3\}\)[/tex]
The correct solution set is [tex]\((x \mid x > 3)\)[/tex].
Thus, the solution set for the inequality [tex]\(-7x < -21\)[/tex] is [tex]\((x \mid x > 3)\)[/tex]. This means that [tex]\( x \)[/tex] must be any number greater than 3.
