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. \( 1-\frac{x}{2}>6 \) A. The solution set in interval notation is 1 (Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.) B. The solution set is \( \varnothing \). an example Get more help -
Ask by Santiago Hills. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set in interval notation is (–∞, –10).
Solution
We start with the inequality:
1 – (x/2) > 6
Step 1. Subtract 1 from both sides:
1 – (x/2) – 1 > 6 – 1
–(x/2) > 5
Step 2. Multiply both sides by –2. Remember that multiplying by a negative number reverses the inequality sign:
x < –10
A. In interval notation, the solution set is:
(–∞, –10)
B. The solution set is not empty.
Graphing on a number line:
• Draw a horizontal number line.
• Place an open circle at –10 (to show –10 is not included).
• Shade or draw an arrow extending to the left from –10 toward –∞.
Thus, the solution to 1 – (x/2) > 6 is x < –10, which in interval notation is (–∞, –10).
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Beyond the Answer
To solve the inequality \( 1 - \frac{x}{2} > 6 \), let's first isolate \( x \). Subtracting 1 from both sides gives us \( -\frac{x}{2} > 5 \). Multiplying both sides by -2 (and flipping the inequality sign) results in \( x < -10 \). Thus, the solution set in interval notation is \( (-\infty, -10) \). Now, graphing this on a number line: draw a line with an open circle at -10, extending leftward indefinitely to represent all numbers less than -10. This visual indicates that every number to the left of -10 is included in your solution set!