Question

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
-2X+2>8 OR -9x-7≤2


0
1
2
3
4
5
-1
-2
-3
-4
-5

Answer 1

To solve the given inequalities, we'll tackle each one separately.

1. **For the first inequality:**
\[
-2x + 2 > 8
\]

We start by isolating \(x\):
\[
-2x > 8 - 2
\]
\[
-2x > 6
\]

Now, divide both sides by \(-2\) (remember to reverse the inequality sign):
\[
x < -3
\]

2. **For the second inequality:**
\[
-9x - 7 \leq 2
\]

Again, we will isolate \(x\):
\[
-9x \leq 2 + 7
\]
\[
-9x \leq 9
\]

Now, divide both sides by \(-9\) (again, reverse the inequality sign):
\[
x \geq -1
\]

Now we have two inequalities:
- From the first inequality: \(x < -3\)
- From the second inequality: \(x \geq -1\)

Since the problem states "OR", we will combine the solution sets. The solution consists of all numbers satisfying either \(x < -3\) or \(x \geq -1\).

### Graphing on the Number Line:
- The solution \(x < -3\) corresponds to an open interval \((-∞, -3)\).
- The solution \(x \geq -1\) corresponds to a closed interval \([-1, ∞)\).

Thus, on the number line, the graph will have:
1. An arrow extending to the left from \(-3\) (indicating all values less than \(-3\)).
2. A solid dot at \(-1\) and an arrow extending to the right (indicating all values greater than or equal to \(-1\)).

### Answer in Interval Notation:
The combined solution in interval notation is:
\[
(-\infty, -3) \cup [-1, \infty)
\]