Jika A X B Adalah Solusi Pertidaksamaan 1 2 X

𝕸𝖆𝖘 𝕬𝖓𝖉𝖞 𝕯𝖎𝖌𝖎𝖙𝖆𝖑 𝕸𝖊𝖉𝖎𝖆

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Apr 07, 2025

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Solving Inequalities: A Complete Guide to Finding Solutions for 1 ≤ 2x

Understanding and solving inequalities is a crucial skill in mathematics. This guide provides a comprehensive approach to solving inequalities, focusing on finding solutions for the specific example: 1 ≤ 2x. We'll break down the process step-by-step, ensuring you grasp the underlying concepts.

Understanding Inequalities

Before diving into the solution, let's clarify what inequalities are. Unlike equations (which use an equals sign =), inequalities use symbols like:

• ≤ (less than or equal to)
• ≥ (greater than or equal to)
• < (less than)
• > (greater than)

These symbols indicate a range of values, rather than a single specific value.

Solving 1 ≤ 2x

Now, let's tackle the inequality 1 ≤ 2x. Our goal is to isolate 'x' to find the range of values that satisfy the inequality.

Step 1: Isolate the variable

To isolate 'x', we need to perform the inverse operation of multiplication (which is division). Divide both sides of the inequality by 2:

1 ≤ 2x
1/2 ≤ (2x)/2
1/2 ≤ x

Step 2: Rewrite the solution

We can rewrite the solution to make it more clear:

x ≥ 1/2  or  x ≥ 0.5

This means that any value of 'x' that is greater than or equal to 0.5 will satisfy the original inequality.

Graphing the Solution

Visualizing the solution can be helpful. We can represent this solution on a number line:

<---●-------->
    0.5

The filled circle at 0.5 indicates that 0.5 is included in the solution set. The arrow pointing to the right shows that all values greater than 0.5 are also part of the solution.

Checking the Solution

It’s always a good idea to check your solution. Let's try a few values:

• x = 0.5: 1 ≤ 2(0.5) => 1 ≤ 1 (True)
• x = 1: 1 ≤ 2(1) => 1 ≤ 2 (True)
• x = 2: 1 ≤ 2(2) => 1 ≤ 4 (True)
• x = 0: 1 ≤ 2(0) => 1 ≤ 0 (False)

The test confirms that our solution, x ≥ 0.5, is correct. Values equal to or greater than 0.5 satisfy the inequality, while values less than 0.5 do not.

Conclusion

Solving inequalities involves manipulating the inequality to isolate the variable, similar to solving equations. Remember to pay attention to the inequality symbols and the impact of operations on the inequality sign. Always check your answer with a few test values to ensure its accuracy. Understanding this process will allow you to confidently tackle various inequality problems. This detailed explanation, along with clear steps and visual aids, makes understanding this mathematical concept easier and more accessible. Remember to practice! The more you solve inequalities, the more proficient you’ll become.