Question
Solve and graph the solution set. \( x+9<5 x-11 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type your answer in interval notation.) B. There is no solution.
Ask by Bartlett Allan. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \( x > 5 \), which in interval notation is \( (5, \infty) \).
Solution
To solve the inequality x + 9 < 5x - 11, follow these steps:
1. Subtract x from both sides:
9 < 4x - 11
2. Add 11 to both sides:
20 < 4x
3. Divide both sides by 4:
5 < x
Thus, the solution is x > 5.
In interval notation, the solution set is (5, ∞).
Graphically, you can represent this solution by drawing a number line, placing an open circle at 5, and shading the line to the right of 5 to indicate that all numbers greater than 5 are included in the solution.
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Simplify this solution Bonus Knowledge
First, let's solve the inequality \( x + 9 < 5x - 11 \). Start by isolating \( x \): 1. Subtract \( x \) from both sides: \[ 9 < 4x - 11 \] 2. Add 11 to both sides: \[ 20 < 4x \] 3. Divide by 4: \[ 5 < x \] This is the same as \( x > 5 \). Now, for the graphing part, you can represent this on a number line with an open circle at 5, indicating that 5 is not included in the solution set, and shade to the right to signify that all numbers greater than 5 are included. The solution set in interval notation is \( (5, \infty) \).
