Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Solve the following inequality:
[tex]\[ -18x + 21 \ \textgreater \ -15 \quad \text{OR} \quad 20x - 13 \geq 27 \][/tex]

Choose one answer:
(A) [tex]\( x \ \textless \ -2 \)[/tex] or [tex]\( x \geq 2 \)[/tex]
(B) [tex]\( x = -2 \)[/tex]
(C) [tex]\( x \geq 2 \)[/tex]
(D) There are no solutions
(E) All values of [tex]\( x \)[/tex] are solutions


Sagot :

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]