Question
Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. \( 6-(x+8) \geq 1-4 x \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \square \). (Type your answer using interval notation.) B. The solution set is \( \varnothing \).
Ask by Chavez Young. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is [1, ∞).
Solution
Step 1: Simplify the inequality
Start with:
6 - (x + 8) ≥ 1 - 4x
Distribute the negative sign inside the parentheses:
6 - x - 8 ≥ 1 - 4x
Combine like terms on the left:
-x - 2 ≥ 1 - 4x
Step 2: Isolate x
Add 4x to both sides to collect the x terms on one side:
3x - 2 ≥ 1
Now, add 2 to both sides:
3x ≥ 3
Divide both sides by 3:
x ≥ 1
Solution in Interval Notation: [1, ∞)
Step 3: Graph on a Number Line
To graph the solution set:
• Mark a solid dot at 1 (indicating that 1 is included in the solution).
• Shade the number line to the right of 1 toward infinity.
Final Answer:
A. The solution set is [1, ∞).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To solve the inequality \( 6 - (x + 8) \geq 1 - 4x \), first simplify it: 1. Distribute: \( 6 - x - 8 \geq 1 - 4x \) 2. Combine like terms: \( -x - 2 \geq 1 - 4x \) 3. Add \( 4x \) to both sides: \( 3x - 2 \geq 1 \) 4. Add \( 2 \) to both sides: \( 3x \geq 3 \) 5. Divide by \( 3 \): \( x \geq 1 \) The solution set is \( [1, \infty) \). For the graph on a number line, mark a closed circle at \( 1 \) and shade to the right towards infinity, indicating all values greater than or equal to \( 1 \) are part of the solution. The solution set is \( [1, \infty) \).
