Question

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
-5x+3≤ 18


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

Answers

Answered by GPT-4o mini
To solve the inequality \(-5x + 3 \leq 18\), we start by isolating \(x\).

1. Subtract 3 from both sides:
\[
-5x \leq 18 - 3
\]
\[
-5x \leq 15
\]

2. Next, divide both sides by \(-5\). Remember that dividing by a negative number reverses the inequality sign:
\[
x \geq \frac{15}{-5}
\]
\[
x \geq -3
\]

Now, we have the solution:
\[
x \geq -3
\]

**Interval Notation**:
The solution in interval notation is:
\[
[-3, \infty)
\]

**Graphing the Solution on a Number Line**:
To represent the solution on a number line:
- Draw a closed dot at \(-3\) to indicate that \(-3\) is included in the solution.
- Shade the line to the right of \(-3\) to indicate all values greater than \(-3\).

Here’s a textual representation:

```
<--|----|----|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2 3 4
●========================>
```

Where ● represents -3, the shaded region extends to the right, indicating all numbers greater than -3.
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