Let's solve the inequality [tex]\( 15x < -45 \)[/tex] step-by-step:
1. Start with the given inequality:
[tex]\[
15x < -45
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex]:
To do this, we need to divide both sides of the inequality by 15. It's important to remember that when dividing by a positive number, the direction of the inequality does not change.
[tex]\[
\frac{15x}{15} < \frac{-45}{15}
\][/tex]
3. Simplify the fractions:
On the left side, [tex]\( \frac{15x}{15} \)[/tex] simplifies to [tex]\( x \)[/tex], and on the right side, [tex]\( \frac{-45}{15} \)[/tex] simplifies to [tex]\( -3 \)[/tex].
[tex]\[
x < -3
\][/tex]
4. Determine the solution set:
The inequality [tex]\( x < -3 \)[/tex] indicates that [tex]\( x \)[/tex] can be any value less than -3.
The correct solution set for the inequality [tex]\( 15x < -45 \)[/tex] is:
[tex]\[
\{x \mid x < -3\}
\][/tex]
So, the solution set is:
[tex]\[
\{x \mid x < -3\}
\][/tex]
