Solve for $x : 2 x -2>4 x +6$

Subtract 2 x from both sides: 2x + 6"> − 2 > 2 x + 6 .
Subtract 6 from both sides: 2x"> − 8 > 2 x .
Divide both sides by 2: x"> − 4 > x .
Rewrite the inequality: x < − 4 . The solution is x < − 4 ​ .

Explanation

Understanding the Problem We are given the inequality 4x + 6"> 2 x − 2 > 4 x + 6 and we want to solve for x .

Subtracting 2x from Both Sides First, let's subtract 2 x from both sides of the inequality: 4x + 6 - 2x"> 2 x − 2 − 2 x > 4 x + 6 − 2 x This simplifies to: 2x + 6"> − 2 > 2 x + 6

Subtracting 6 from Both Sides Next, subtract 6 from both sides of the inequality: 2x + 6 - 6"> − 2 − 6 > 2 x + 6 − 6 This simplifies to: 2x"> − 8 > 2 x

Dividing by 2 Now, divide both sides of the inequality by 2: \frac{2x}{2}"> 2 − 8 ​ > 2 2 x ​ This simplifies to: x"> − 4 > x

Rewriting the Inequality Finally, we can rewrite the inequality as: x < − 4

Final Answer Therefore, the solution to the inequality is x < − 4 .


Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, when budgeting, you might use inequalities to determine how much you can spend on different items while staying within your financial limits. Similarly, in science, inequalities can help define the range of acceptable values for experimental parameters to ensure accurate results. This problem demonstrates a fundamental skill in algebra that has broad applications.

Answered by GinnyAnswer | 2025-07-05