Given:
Which of the following statements is necessarily true?
We have hundreds of course questions with personalized recommendations + Account 100% premium
Given:
Which of the following statements is necessarily true?
To solve the inequality , we will apply the property of absolute values by rewriting it without the absolute value sign as follows:
Step 1: Transform the absolute value inequality
Using the rule implies , we write
.
Step 2: Solve this compound inequality. We do this by isolating as follows:
Thus, the inequality is solved as .
The correct solution is contained in choice 3: .
Given:
\( \left|2x-1\right|>-10 \)
Which of the following statements is necessarily true?
The absolute value represents the distance from zero. When this distance is less than 3, the expression inside must be between -3 and 3!
You're on the right track! But remember, both conditions must be true simultaneously. Write it as one compound inequality: .
Pick any number in your interval (like x = 0) and substitute: ✓. Also test the boundaries to make sure they're not included!
With < (strict inequality), the boundary values are not included. Use open circles on number lines. With ≤, the boundary values are included - use closed circles.
That's a common error! When you have -3 < x + 2 < 3, you must subtract 2 from all three parts: -3 - 2 < x < 3 - 2, giving -5 < x < 1.
Get unlimited access to all 18 Absolute Value and Inequality questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime