Question
\( -9 \leq x+2<9 \) Isolate \( x \) in the compound inequality. sel. numbers in the expression.) Select the correct choice below and, if necessary, fill in the answer box to notation for the solution set. Then graph the solution complete your choice. A. The solution set in interval notation is \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no solution.
Ask by Mcfarlane Watkins. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set in interval notation is [–11, 7).
Solution
We start with the compound inequality:
–9 ≤ x + 2 < 9
Step 1: Subtract 2 from all parts to isolate x:
–9 – 2 ≤ x + 2 – 2 < 9 – 2
–11 ≤ x < 7
Step 2: Write the solution set in interval notation:
The solution set is [–11, 7).
Step 3: Graph the solution:
• Place a closed (filled) circle at –11.
• Place an open circle at 7.
• Shade the line between –11 and 7.
This completes the isolation and representation of x.
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Simplify this solution Mind Expander
To isolate \( x \) in the compound inequality \( -9 \leq x+2 < 9 \), we first subtract 2 from all parts of the inequality: \[ -9 - 2 \leq x + 2 - 2 < 9 - 2 \] This simplifies to: \[ -11 \leq x < 7 \] So the solution set in interval notation is \( [-11, 7) \). For the graph of the solution, you would represent it on a number line where the point -11 is included (closed dot) and the point 7 is not included (open dot).
