Watch the video and then solve the problem given below. Click here to watch the video. Solve and graph the compound inequality. \( -7

Ask by Paul Parry. in the United States

Feb 25,2025

To solve the compound inequality \( -7 < x + 1 < 10 \), we will break it down into two separate inequalities and solve them step by step. ### Step 1: Solve the first inequality The first part of the compound inequality is: \[ -7 < x + 1 \] To isolate \( x \), we subtract 1 from both sides: \[ -7 - 1 < x \] \[ -8 < x \] This can be rewritten as: \[ x > -8 \] ### Step 2: Solve the second inequality The second part of the compound inequality is: \[ x + 1 < 10 \] Again, we isolate \( x \) by subtracting 1 from both sides: \[ x < 10 - 1 \] \[ x < 9 \] ### Step 3: Combine the results Now we combine the results from both inequalities: \[ -8 < x < 9 \] ### Step 4: Write the solution in interval notation The solution set in interval notation is: \[ (-8, 9) \] ### Step 5: Graph the solution To graph the solution, we will represent the interval \((-8, 9)\) on a number line. The endpoints \(-8\) and \(9\) are not included in the interval, so we will use open circles at these points. Now, I will graph the solution. ### Final Answer A. The solution set in interval notation is \((-8, 9)\). If you need the graph, please let me know!