Solve the following inequality.
−
5
x
−
3
≥
−
x
+
9

Give your answer in interval notation. For example, if you found
x
<
20
, you would enter
(
−
∞
,
20
)
.

Let's solve the inequality:

\[
-5x - 3 \geq -x + 9
\]

### Step 1: Move all terms involving \( x \) to one side of the inequality.

Add \( 5x \) to both sides:

\[
-3 \geq 4x + 9
\]

### Step 2: Move constant terms to the other side.

Subtract 9 from both sides:

\[
-12 \geq 4x
\]

### Step 3: Solve for \( x \).

Now, divide both sides by 4:

\[
x \leq -3
\]

### Step 4: Express the solution in interval notation.

The solution is:

\[
(-\infty, -3]
\]

Would you like any more details or have any questions about the steps?

Here are 5 related questions to explore:
1. How do you solve inequalities with fractions?
2. What changes when multiplying both sides of an inequality by a negative number?
3. How can you solve a quadratic inequality?
4. What does it mean if an inequality has no solution?
5. How do you express the union of two intervals?

**Tip:** Always flip the inequality sign when multiplying or dividing by a negative number.

Solve the following inequality. -5x - 3 ≥ -x + 9. Give your answer in interval notation. For example, if you found x < 20, you would enter (-∞, 20).

This detailed guide walks you through solving the inequality -5x - 3 ≥ -x + 9 step by step. Learn key algebra concepts like linear inequality manipulation, and find out how to express the solution in interval notation. Perfect for Grades 8-10 students looking to understand inequalities better.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation