Let's solve the given inequalities step-by-step to determine the values of [tex]\( x \)[/tex].
1. Solve the first inequality:
[tex]\[
-18x + 21 > -15
\][/tex]
- First, isolate the term involving [tex]\( x \)[/tex]. Subtract 21 from both sides:
[tex]\[
-18x > -15 - 21
\][/tex]
[tex]\[
-18x > -36
\][/tex]
- Next, solve for [tex]\( x \)[/tex] by dividing both sides of the inequality by [tex]\(-18\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[
x < \frac{-36}{-18}
\][/tex]
[tex]\[
x < 2
\][/tex]
The solution to the first inequality is:
[tex]\[
x < 2
\][/tex]
2. Solve the second inequality:
[tex]\[
20x - 13 \geq 27
\][/tex]
- First, isolate the term involving [tex]\( x \)[/tex]. Add 13 to both sides:
[tex]\[
20x \geq 27 + 13
\][/tex]
[tex]\[
20x \geq 40
\][/tex]
- Next, solve for [tex]\( x \)[/tex] by dividing both sides of the inequality by 20:
[tex]\[
x \geq \frac{40}{20}
\][/tex]
[tex]\[
x \geq 2
\][/tex]
The solution to the second inequality is:
[tex]\[
x \geq 2
\][/tex]
3. Combine the solutions from both inequalities:
[tex]\[
x < 2 \quad \text{or} \quad x \geq 2
\][/tex]
This combination of solutions indicates that [tex]\( x \)[/tex] can either be less than 2 or greater than or equal to 2.
Therefore, the correct choice is:
(A) [tex]\( x < -2 \)[/tex] or [tex]\( x \geq 2 \)[/tex]
