Answered

Join IDNLearn.com and start getting the answers you've been searching for. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.

Solve the compound inequality for [tex]\( x \)[/tex]:

[tex]\[ 6x + 2 \ \textgreater \ 14 \text{ or } 3x - 1 \ \textless \ 2 \][/tex]

Select one:
A. [tex]\( x \ \textgreater \ \frac{16}{6} \)[/tex] or [tex]\( x \ \textless \ \frac{1}{3} \)[/tex]
B. [tex]\( x \ \textgreater \ 2 \)[/tex] or [tex]\( x \ \textless \ 1 \)[/tex]
C. [tex]\(-2 \ \textless \ x \ \textgreater \ 1 \)[/tex]
D. [tex]\( x \ \textgreater \ -2 \)[/tex] and [tex]\( x \ \textless \ -1 \)[/tex]

Sagot :

GinnyAnsweridn
To solve the compound inequality [tex]\( 6x + 2 > 14 \text{ or } 3x - 1 < 2 \)[/tex], you need to solve each inequality separately and then combine their results logically.

1. Solve the inequality [tex]\( 6x + 2 > 14 \)[/tex]:
[tex]\[ 6x + 2 > 14 \][/tex]
Subtract 2 from both sides:
[tex]\[ 6x > 12 \][/tex]
Divide both sides by 6:
[tex]\[ x > 2 \][/tex]

2. Solve the inequality [tex]\( 3x - 1 < 2 \)[/tex]:
[tex]\[ 3x - 1 < 2 \][/tex]
Add 1 to both sides:
[tex]\[ 3x < 3 \][/tex]
Divide both sides by 3:
[tex]\[ x < 1 \][/tex]

Now, combine the results of the two inequalities:
- From the first inequality, we have [tex]\( x > 2 \)[/tex].
- From the second inequality, we have [tex]\( x < 1 \)[/tex].

Therefore, the solution to the compound inequality [tex]\( 6x + 2 > 14 \text{ or } 3x - 1 < 2 \)[/tex] is:
- [tex]\( x > 2 \)[/tex] or [tex]\( x < 1 \)[/tex].

So, the correct answer is:
b. [tex]\( x > 2 \)[/tex] or [tex]\( x < 1 \)[/tex].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.