Math Problem Statement

Solve the inequality: 4c < 14 - 3c.

Solution

Let's solve the inequality:

Given:

4c<143c4c < 14 - 3c

Step 1: Add 3c3c to both sides to eliminate 3c3c on the right-hand side:

4c+3c<144c + 3c < 14 7c<147c < 14

Step 2: Divide both sides by 77 to isolate cc:

c<147c < \frac{14}{7} c<2c < 2

Final Answer:

The solution to the inequality is: c<2c < 2

Let me know if you'd like further details or have any questions!


Follow-up Questions:

  1. What are the key differences between solving equations and inequalities?
  2. How would the solution change if the inequality symbol were >> instead of <<?
  3. What happens when you multiply or divide by a negative number in inequalities?
  4. Can you graph this solution on a number line? How would it look?
  5. How do you check whether a value satisfies an inequality?

Tip:

When solving inequalities, remember to reverse the inequality sign if you multiply or divide by a negative number!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Equations

Formulas

Basic inequality manipulation

Theorems

Properties of inequalities (e.g., adding, subtracting, dividing both sides)

Suitable Grade Level

Grades 7-9