Graph the solution and write the set in interval notation.
3≤t-4≤5
Part 1 of 2
The graph of the solution set is
To graph the solution set, we need to plot the numbers that satisfy the inequality. Let's start by solving the inequality.
3 ≤ t - 4 ≤ 5
Add 4 to all sides of the inequality:
3 + 4 ≤ t - 4 + 4 ≤ 5 + 4
7 ≤ t ≤ 9
The solution set is all the numbers between 7 and 9, including 7 and 9. These numbers are:
{t | 7 ≤ t ≤ 9}
To graph this solution set, we can create a number line. We mark points at 7 and 9, and shade the region between these points.
7 9
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To graph the solution set for the inequality 3 ≤ t - 4 ≤ 5, we can start by isolating t in the middle of the inequality.
Adding 4 to all parts of the inequality, we get:
3 + 4 ≤ t - 4 + 4 ≤ 5 + 4
Which simplifies to:
7 ≤ t ≤ 9
Now, we can graph the solution set on a number line. Mark a point at 7 and shade all the points from 7 to 9, including both endpoints.
On the number line, the graph would look like this:
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7 9
The shaded region represents the solution set for the inequality.
Now, let's write the solution set in interval notation.
The solution set in interval notation is [7, 9].