Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
Either [tex]x > 2[/tex], or [tex]x < -10[/tex].
Step-by-step explanation:
Make use of the following property of absolute value inequalities: given a positive number [tex]p[/tex] ([tex]p > 0[/tex]) and some algebraic expression [tex]X[/tex], the following are equivalent:
- [tex]|X| > p[/tex], and
- either [tex]X < (-p)[/tex] or [tex]X > p[/tex].
In this question, [tex]| (x + 4) / 3| > 2[/tex] would be equivalent to [tex]((x + 4) / 3) > 2[/tex] or [tex]((x + 4) / 3) < -2[/tex]. Simplify to separate [tex]x[/tex]:
[tex]\displaystyle \frac{x + 4}{3} > 2 \quad \text{or} \quad \frac{x + 4}{3} < -2[/tex].
[tex]x + 4 > 6 \quad \text{or} \quad x + 4 < -6[/tex].
[tex]x > 2 \quad \text{or} \quad x < -10[/tex].
In other words, the given inequality is satisfied if and only if either [tex]x > 2[/tex] or [tex]x < -10[/tex].
The final solution is x < -10 or x > 2.
To solve the inequality, we need to break it down into two separate inequalities:
1. (x+4)/3 > 2
2. (x+4)/3 < -2
Solve (x+4)/3 > 2:
- Multiply both sides by 3:
(x+4)/3 *3 > 2 * 3
(x+4) > 6
- Subtract 4 from both sides:
(x+4) - 4 > 6 - 4
x > 2
Solve (x+4)/3 < -2:
- Multiply both sides by 3:
(x+4)/3 *3 < -2 * 3
(x+4) < -6
- Subtract 4 from both sides:
(x+4) - 4 < -6 - 4
x < -10
Thus, the solution to the inequality |(x+4)/3| > 2 is x < -10 or x > 2.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.