4x-4 2 solve the inequality

Lyra Rowan

2 min read

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29-09-2024

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Solving the Inequality: 4x - 4 < 2

This article will guide you through solving the inequality 4x - 4 < 2, explaining each step clearly and providing insights into the underlying principles. We'll also explore the significance of inequalities and their applications in real-world scenarios.

Understanding the Inequality:

The inequality 4x - 4 < 2 means we are looking for all values of 'x' that, when plugged into the expression 4x - 4, result in a value less than 2. To solve this, we need to isolate 'x' on one side of the inequality.

Steps to Solve:

1. Add 4 to both sides: This eliminates the constant term on the left side.

   • 4x - 4 + 4 < 2 + 4
   • 4x < 6

2. Divide both sides by 4: This isolates 'x' and gives us the solution.

   • 4x / 4 < 6 / 4
   • x < 1.5

Solution:

The solution to the inequality 4x - 4 < 2 is x < 1.5. This means any value of 'x' less than 1.5 will satisfy the original inequality.

Visualizing the Solution:

We can represent the solution graphically on a number line. Draw a number line and mark 1.5 on it. Since the solution is 'x < 1.5', we use an open circle at 1.5 (indicating that 1.5 is not included in the solution) and shade the line to the left of 1.5, representing all values less than 1.5.

Practical Applications:

Inequalities are used widely in various fields, including:

• Economics: Inequalities can describe relationships between supply and demand, prices, and profits.
• Engineering: Inequalities are used in design constraints for structures, machines, and systems.
• Physics: Inequalities are used in calculations related to motion, energy, and forces.

Example:

Imagine a scenario where a car rental company charges a base fee of $4 and an additional $4 per hour for rental. You have a budget of $10. The inequality 4x - 4 < 10 (where 'x' represents the number of hours you can rent the car) would allow you to determine how many hours you can rent the car within your budget. Solving this inequality, you find that you can rent the car for less than 3.5 hours.

In Conclusion:

Solving inequalities involves isolating the variable on one side of the inequality sign. The solution to the inequality 4x - 4 < 2 is x < 1.5. Understanding inequalities is crucial in various fields as they help us analyze and solve real-world problems.

Note: This article incorporates a concept from BrainlY but expands upon it with explanations, visuals, and practical examples to make it more informative and engaging for readers.