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.)

Solve the inequality by following steps: - step0: Solve for \(x\): \(9x+2<8x-3\) - step1: Move the expression to the left side: \(9x-8x<-3-2\) - step2: Add and subtract: \(x<-3-2\) - step3: Add and subtract: \(x<-5\) To solve the inequality \( 9x + 2 < 8x - 3 \), we can follow these steps: 1. **Isolate the variable \( x \)**: - Subtract \( 8x \) from both sides: \[ 9x - 8x + 2 < -3 \] This simplifies to: \[ x + 2 < -3 \] 2. **Subtract 2 from both sides**: \[ x < -3 - 2 \] This simplifies to: \[ x < -5 \] The solution set in interval notation is: \[ (-\infty, -5) \] ### Graphing the Solution While I cannot provide a graph directly, you can visualize the solution as follows: - Draw a number line. - Mark the point \(-5\) on the line. - Shade the region to the left of \(-5\) to indicate that all values less than \(-5\) are included in the solution set. Thus, the final answer is: \[ \text{The solution set is } (-\infty, -5). \]