Question
Solve the inequality \( 9 x+2<8 x-3 \). Write the solution set in interval notation, and graph it. The solution set is \( \square \). (Type your answer in interval notation.)
Ask by Hodges Stephens. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \( (-\infty, -5) \).
Solution
To solve the inequality 9x + 2 < 8x - 3, follow these steps:
1. Subtract 8x from both sides:
9x - 8x + 2 < -3
x + 2 < -3
2. Subtract 2 from both sides:
x < -5
Thus, the solution set is all x such that x is less than -5.
In interval notation, the solution set is: (-∞, -5).
Graph:
On a number line, mark an open circle at -5 and shade all numbers extending to the left (toward -∞).
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Simplify this solution The Deep Dive
To solve the inequality \( 9x + 2 < 8x - 3 \), we can start by isolating \( x \). Subtract \( 8x \) from both sides: \[ 9x - 8x + 2 < -3 \] \[ x + 2 < -3 \] Next, we subtract 2 from both sides: \[ x < -5 \] The solution set in interval notation is \( (-\infty, -5) \). To graph this solution, you would draw a number line with an open circle at -5 (indicating -5 is not included) and shade the line to the left, indicating all values less than -5 are included in the solution set.
