Question

Solve and graph the compound inequality.

2x + 1 ≤ 7 and -2x + 1 ≤ 9
A
B
C
D

Answer 1

To solve the compound inequality 2x + 1 ≤ 7 and -2x + 1 ≤ 9, we need to solve each inequality separately and then find the intersection of both solutions, as both conditions must be true at the same time.

Let's start by solving each inequality:

1. Solve 2x + 1 ≤ 7
Subtract 1 from both sides: 2x ≤ 6
Divide both sides by 2: x ≤ 3

2. Solve -2x + 1 ≤ 9
Subtract 1 from both sides: -2x ≤ 8
Divide both sides by -2 (remember to flip the inequality sign when dividing by a negative): x ≥ -4

Now, to find the solution to the compound inequality, we look for values of x that satisfy both conditions:

x ≤ 3 (from the first inequality)
x ≥ -4 (from the second inequality)

The intersection of both solutions is the set of all x values that are between -4 and 3, inclusive:

-4 ≤ x ≤ 3

To graph this compound inequality on a number line, you would:

1. Draw a number line.
2. Put a closed dot on -4 and a closed dot on 3 (closed dots because the inequalities include the endpoints).
3. Shade the region between -4 and 3 to indicate that all those values satisfy the inequality.

Here is a conceptual representation of the graph using text (since I can't actually draw):

----(-4)===========(3)----A

- The closed interval is marked with "=" signs between -4 and 3 to indicate that the solution includes all numbers between and including those endpoints.
- "A" indicates you provided response choices, but the correct solution and graph description is as provided.