Question

Solve the inequality. Graph and check your solution.
negative 2hless than or equals20
Question content area bottom
Part 1
The solution is h
▼
less than
greater than
greater than or equals
less than or equals
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To solve the inequality \(-2h \leq 20\), we first isolate \(h\) by dividing both sides of the inequality by -2. Remember that when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.

Here are the steps:

1. Start with the inequality:
\[
-2h \leq 20
\]

2. Divide both sides by -2 and flip the inequality sign:
\[
h \geq \frac{20}{-2}
\]

3. Simplify the right side:
\[
h \geq -10
\]

So, the solution is:
\[
h \geq -10
\]

**Part 1 Answer:**
The solution is \(h\) **greater than or equals** \(-10\).

### Graphing the Solution:
On a number line, you would:

1. Place a closed circle at \(-10\) (because it is inclusive, given the "greater than or equals" part).
2. Shade to the right to indicate all numbers greater than or equal to \(-10\).

### Checking the Solution:
To verify, we can test a couple of values:

- **Test \(h = -10\)**:
\[
-2(-10) = 20 \quad \text{(True since \(20 \leq 20\))}
\]

- **Test \(h = 0\)**:
\[
-2(0) = 0 \quad \text{(True since \(0 \leq 20\))}
\]

- **Test \(h = -11\)**:
\[
-2(-11) = 22 \quad \text{(False since \(22 \leq 20\) is not true)}
\]

Thus, the solution \(h \geq -10\) checks out.