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. \( 5 x-9 \geq 26 \) A. The solution set in interval notation is (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in 1 interval notation.) B. The solution set is \( \varnothing \).
Ask by Bolton Parsons. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set in interval notation is [7, ∞).
Solution
We begin with the inequality:
5x – 9 ≥ 26
Step 1. Add 9 to both sides:
5x – 9 + 9 ≥ 26 + 9
5x ≥ 35
Step 2. Divide both sides by 5:
x ≥ 7
A. In interval notation, the solution set is [7, ∞).
B. The statement that the solution set is ∅ (the empty set) is incorrect.
Graphing on a number line:
• Mark a closed (filled-in) circle at 7.
• Shade the line to the right of 7, extending toward infinity.
Thus, the correct solution set in interval notation is [7, ∞).
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Simplify this solution Beyond the Answer
To solve the inequality \( 5x - 9 \geq 26 \), we first add 9 to both sides, yielding \( 5x \geq 35 \). Then, we divide both sides by 5, giving us \( x \geq 7 \). Therefore, the solution set in interval notation is \([7, \infty)\). On the number line, you would represent this interval by placing a closed dot on 7 to indicate that 7 is included in the solution set and shading all the points to the right towards infinity.
