Let's solve the inequality \(-2.7 + 3.1(1 - x) \leq 9.7\).

### Step 1: Distribute the \(3.1\) across the terms inside the parentheses.

\[
-2.7 + 3.1 \cdot 1 - 3.1 \cdot x \leq 9.7
\]

This simplifies to:

\[
-2.7 + 3.1 - 3.1x \leq 9.7
\]

### Step 2: Combine like terms on the left side.

\[
0.4 - 3.1x \leq 9.7
\]

### Step 3: Isolate the \(x\) term by subtracting \(0.4\) from both sides.

\[
-3.1x \leq 9.7 - 0.4
\]

\[
-3.1x \leq 9.3
\]

### Step 4: Solve for \(x\) by dividing both sides by \(-3.1\). Remember, dividing by a negative number reverses the inequality sign.

\[
x \geq \frac{9.3}{-3.1}
\]

\[
x \geq -3
\]

### Final Answer:
The solution to the inequality is \(x \geq -3\).

Do you want more details or have any questions?

Here are 5 related questions:
1. How do you solve inequalities involving absolute values?
2. Can you explain how to graph the solution \(x \geq -3\) on a number line?
3. What happens when both sides of an inequality have variables?
4. How does the solution change if the inequality was \(x \leq -3\) instead?
5. How can you check if a value satisfies the inequality?

**Tip:** When dealing with inequalities, always remember that multiplying or dividing both sides by a negative number reverses the direction of the inequality.

Learn how to solve the inequality -2.7 + 3.1(1 - x) ≤ 9.7 with a detailed step-by-step solution. This problem covers key concepts in inequalities and linear equations, including the distributive property. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation