Question
1.7 Solve Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. \( -6 x \leq 30 \) 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 Hammond Long. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \([-5, \infty)\).
Solution
To solve the inequality –6x ≤ 30, follow these steps:
1. Divide both sides by –6. Remember that dividing by a negative number reverses the inequality sign:
–6x ≤ 30
x ≥ 30/(-6)
2. Simplify the fraction:
x ≥ -5
The solution in interval notation is [-5, ∞). The graph on a number line would have a closed circle at -5 with shading extending to the right.
Thus, the correct choice is:
A. The solution set is [-5, ∞).
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Simplify this solution Bonus Knowledge
To solve the inequality \( -6x \leq 30 \), first, divide both sides by -6. Remember, when you divide by a negative number, you flip the inequality sign. So, we get \( x \geq -5 \). In interval notation, the solution set is \( [-5, \infty) \). To graph this solution set on a number line, draw a solid dot at -5 (indicating that -5 is included), and shade the line extending to the right towards positive infinity, showing all numbers greater than or equal to -5 are part of the solution.
