Solve the Linear Inequality: 2x-5 > 3 Step-by-Step

Linear Inequalities with Basic Operations

Solve the following inequality:

2x5>3 2x-5 > 3

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following inequality:

2x5>3 2x-5 > 3

2

Step-by-step solution

To solve the inequality 2x5>3 2x-5 > 3 , follow these steps:

1. Add 5 to both sides: 2x>8 2x > 8 .

2. Divide both sides by 2: x>4 x > 4 .

3

Final Answer

x>4 x > 4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Perform same operation on both sides to maintain inequality
  • Technique: Add 5 first: 2x-5+5 > 3+5 becomes 2x > 8
  • Check: Test x=5: 2(5)-5 = 5 > 3, so x > 4 works ✓

Common Mistakes

Avoid these frequent errors
  • Flipping inequality sign when dividing by positive numbers
    Don't flip the > to < when dividing 2x > 8 by positive 2 = wrong answer x < 4! The inequality sign only flips when multiplying or dividing by negative numbers. Always keep the same direction when dividing by positive numbers.

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

\( 3x+4 \leq 10 \)

FAQ

Everything you need to know about this question

When do I need to flip the inequality sign?

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You only flip the inequality sign when multiplying or dividing both sides by a negative number. Since we divided by positive 2 in this problem, the sign stays the same!

How can I check if my answer is correct?

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Pick any number greater than 4 (like x = 5) and substitute it back: 2(5)5=5>3 2(5) - 5 = 5 > 3 . Since this is true, our solution x>4 x > 4 is correct!

What's the difference between > and ≥?

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> means "greater than" (doesn't include the boundary), while means "greater than or equal to" (includes the boundary). Our answer uses > because 4 itself doesn't satisfy the original inequality.

Can I solve this inequality in a different order?

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Yes! You could divide by 2 first: x2.5>1.5 x - 2.5 > 1.5 , then add 2.5. Both methods give the same answer: x>4 x > 4 .

Why is the answer x > 4 and not just x = 4?

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Because we have an inequality (>) not an equation (=). This means x can be any number greater than 4, like 4.1, 5, 10, or 100!

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