Question
Part 1 of 2 (8) Points: 0.5 of 1 Save Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. \[ -6 x \geq 42 \] 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 \( \varnothing \). w an example Get more help - Clear all Check answer
Ask by Powers Crawford. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \( (-\infty, -7] \).
Solution
We start with the inequality: -6x ≥ 42.
Step 1: Divide both sides by -6. Remember that when you divide or multiply an inequality by a negative number, the inequality sign reverses.
x ≤ 42/(-6)
Step 2: Simplify the right-hand side:
42/(-6) = -7
So the solution is:
x ≤ -7
In interval notation, the solution set is:
(-∞, -7]
To graph on a number line, draw a closed circle at -7 and shade the line to the left (indicating all numbers less than or equal to -7).
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Simplify this solution The Deep Dive
To solve the inequality \(-6x \geq 42\), first divide both sides by -6, remembering to reverse the inequality sign. This gives you: \[ x \leq -7 \] In interval notation, the solution set is \((-\infty, -7]\). Now, to graph this on a number line: Draw a line and mark the point at -7 with a closed dot (to indicate that -7 is included in the solution set). Then shade everything to the left of -7 to indicate all the numbers less than or equal to -7 are included in the solution. So, the answer is: A. The solution set is \((-\infty, -7]\).
