Question

Step 1: Solve and graph this inequality:



`-5\left(x+2\right)\ge-45`

Answers

GPT-4o mini
To solve the inequality \(-5(x + 2) \ge -45\), follow these steps:

### Step 1: Distribute the -5
Distributing \(-5\) gives:
\[
-5x - 10 \ge -45
\]

### Step 2: Add 10 to both sides
Now, add \(10\) to both sides to isolate the term with \(x\):
\[
-5x - 10 + 10 \ge -45 + 10
\]
This simplifies to:
\[
-5x \ge -35
\]

### Step 3: Divide by -5
When dividing by a negative number, remember to reverse the inequality sign:
\[
x \le \frac{-35}{-5}
\]
This simplifies to:
\[
x \le 7
\]

### Step 4: Graph the inequality
To graph \(x \le 7\):
1. Draw a number line.
2. Locate the point \(7\) on the line.
3. Place a closed dot on \(7\) (indicating that \(7\) is included in the solution).
4. Shade to the left from \(7\) to indicate all values less than \(7\).

### Final Answer:
The solution to the inequality is \(x \le 7\), and the graph reflects this as described above.