What is the solution of x-4 is less than 4 and x + 4 is greater than 7
Please show how you did it so I can look at it and learn how to do them in the future
Thanks
To solve the given inequality "x - 4 < 4" and "x + 4 > 7," let's solve each inequality separately and then analyze the results.
1. x - 4 < 4:
- Add 4 to both sides of the inequality: x - 4 + 4 < 4 + 4.
- Simplify: x < 8.
2. x + 4 > 7:
- Subtract 4 from both sides of the inequality: x + 4 - 4 > 7 - 4.
- Simplify: x > 3.
Now, we have two inequalities: x < 8 and x > 3.
To find the solution that satisfies both inequalities, we need to find the common region where they overlap on a number line.
1. Draw a number line with an arrow extending in both directions.
2. Mark the number 8 with an open circle on the line. This represents x < 8.
3. Mark the number 3 with an open circle on the line. This represents x > 3.
4. Shade the region between these two numbers (3 and 8) on the number line.
The shaded region represents the solution set of the inequality system "x - 4 < 4" and "x + 4 > 7". In this case, the solution set is x > 3 and x < 8, where x belongs to real numbers.
To summarize, the solution to the given inequality system is 3 < x < 8, or in interval notation, (-∞, 8) ∩ (3, +∞).