Question
Watch the video and then solve the problem given below.
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Solve and graph the compound inequality.
\( -4
Ask by Ball Burgess. in the United States
Feb 25,2025
Ask by Ball Burgess. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the inequality –4 < x + 4 < 8 is –8 < x < 4. On the number line, this is represented by shading the region between –8 and 4, with open circles at –8 and 4 to indicate that these points are not included.
Solution
To solve the compound inequality
–4 < x + 4 < 8,
follow these steps:
Step 1: Subtract 4 from all three parts of the inequality to isolate x.
–4 – 4 < x + 4 – 4 < 8 – 4
Step 2: Simplify each part:
–8 < x < 4
So, the solution is x is greater than –8 and less than 4. In interval notation, this is written as (–8, 4).
Graph on a Number Line:
1. Draw a horizontal number line and mark –8 and 4.
2. Place an open circle at –8 and another at 4 (indicating that –8 and 4 are not included).
3. Shade the line between –8 and 4.
This represents all the values of x that satisfy –8 < x < 4.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To solve the compound inequality \( -4 < x + 4 < 8 \), we can break it into two parts and solve for \( x \). First, we subtract 4 from all parts of the inequality: 1. Starting with \( -4 < x + 4 \): \(-4 - 4 < x\) \(-8 < x\) or \( x > -8\) 2. Now the second part, \( x + 4 < 8 \): \(x < 8 - 4\) \(x < 4\) Combining these results, we get the final inequality: \(-8 < x < 4\) To graph this inequality, draw a number line and place open circles at -8 and 4 to indicate that these values are not included in the solution, shading the region between them. Now, if you have additional questions or need help with another problem, feel free to ask!
