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].
