Question

Solve the compound inequality. Express the solution using interval notation.

3x-2≤13 and 4-x< - 2

Answer 1

1. Solve the first inequality:
3x - 2 ≤ 13

Add 2 to both sides:
3x ≤ 15

Divide by 3 (since 3 is positive, we don’t need to reverse the inequality sign):
x ≤ 5

2. Solve the second inequality:
4 - x < -2

Subtract 4 from both sides:
-x < -2 - 4
-x < -6

Multiply by -1 (since we’re multiplying by a negative number, we need to reverse the inequality sign):
x > 6

Now, let’s combine the solutions of both inequalities:

x ≤ 5 and x > 6

To express this compound inequality using interval notation, you can break it into two separate intervals:

1. For the first part (x ≤ 5), the interval is:
(-∞, 5]
2. For the second part (x > 6), the interval is:
(6, ∞)

So, the solution in interval notation is:
(-∞, 5] ∪ (6, ∞)