Math Problem Statement

Solve: 3𝑦 + 𝑥 < 7𝑥 + 6.

Responses

y < 2𝑥 + 2

y < 2𝑥 + 2

y < 2𝑥 + 1

y < 2𝑥 + 1

y < 3𝑥 + 1

y < 3𝑥 + 1

y < −2𝑥 + 2

Solution

Let's solve the inequality step by step:

Given inequality:

3y+x<7x+63y + x < 7x + 6

Step 1: Isolate terms with yy

We want to move the xx-related terms to the other side of the inequality.

3y<7xx+63y < 7x - x + 6

Simplifying the terms: 3y<6x+63y < 6x + 6

Step 2: Solve for yy

Now, divide both sides by 3 to isolate yy:

y<6x+63y < \frac{6x + 6}{3}

Simplifying the right-hand side:

y<2x+2y < 2x + 2

Conclusion:

The solution is: y<2x+2y < 2x + 2

This corresponds to the first two responses.


Would you like a more detailed explanation on this? Here are five additional questions based on this topic:

  1. How do we solve an inequality differently from an equation?
  2. What changes when we multiply or divide an inequality by a negative number?
  3. How would this inequality look if solved for xx instead of yy?
  4. Can inequalities like this be represented graphically? If so, how?
  5. How do we deal with compound inequalities involving both xx and yy?

Tip: Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Linear inequality solving: ax + b < cx + d

Theorems

Properties of inequalities
Addition and multiplication properties of inequalities

Suitable Grade Level

Grades 8-10