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:
Step 1: Isolate terms with
We want to move the -related terms to the other side of the inequality.
Simplifying the terms:
Step 2: Solve for
Now, divide both sides by 3 to isolate :
Simplifying the right-hand side:
Conclusion:
The solution is:
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:
- How do we solve an inequality differently from an equation?
- What changes when we multiply or divide an inequality by a negative number?
- How would this inequality look if solved for instead of ?
- Can inequalities like this be represented graphically? If so, how?
- How do we deal with compound inequalities involving both and ?
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