Let's solve the inequality step by step.

The inequality is:

\[
-65y + 19 < -2y + 41
\]

### Step 1: Move the \(y\)-terms to one side.
Add \(65y\) to both sides to eliminate the \(y\)-term on the left side:

\[
19 < 63y + 41
\]

### Step 2: Move the constants to the other side.
Subtract \(41\) from both sides to isolate the \(y\)-term:

\[
19 - 41 < 63y
\]

This simplifies to:

\[
-22 < 63y
\]

### Step 3: Solve for \(y\).
Divide both sides by \(63\) to isolate \(y\):

\[
\frac{-22}{63} < y
\]

Thus, the solution is:

\[
y > \frac{-22}{63}
\]

or approximately:

\[
y > -0.349
\]

### Final Answer:
The solution is:

\[
y > \frac{-22}{63}
\]

Would you like further clarification, or do you have any questions?

---

Here are 5 related questions:
1. How would the solution change if the inequality were \( -65y + 19 > -2y + 41 \)?
2. What happens if you multiply or divide an inequality by a negative number?
3. Can you graph the solution \( y > \frac{-22}{63} \) on a number line?
4. How would you solve the inequality if it had fractions instead of integers?
5. What is the general process for solving a system of inequalities?

**Tip:** When solving inequalities, always remember to reverse the inequality sign if you multiply or divide both sides by a negative number.

Learn how to solve the inequality -65y + 19 < -2y + 41 with a detailed step-by-step solution. This example covers key algebraic concepts like isolating variables and dividing inequalities. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation