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

Q: What if I get confused with the algebra steps?

Take it slow: First collect like terms (get all x terms together), then isolate the variable. Write each step clearly: 5x + b > 2x + 3 → 3x + b > 3 → 3x > 3 - b → x > (3-b)/3

Q: Does the inequality direction ever change in this problem?

No! We only subtract terms and divide by positive 3, so the inequality direction stays the same throughout. The > symbol never flips to

Q: Can I solve this graphically?

Yes! Graph $ y = 5x + b $ and $ y = 2x + 3 $. The solution is where the first line is above the second line (to the right of their intersection point).

Linear Inequalities with Parameter Variables

Solve the inequality:

$5x+b > 2x+3$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the inequality:

$5x+b > 2x+3$

Step-by-step solution

To solve the inequality $5x+b > 2x+3$ , we will follow these steps:

Subtract $2x$ from both sides: $3x + b > 3$
Subtract $b$ from both sides: $3x > 3 - b$
Divide both sides by $3$ : $x > -\frac{1}{3}b + 1$

Final Answer

$x > -\frac{1}{3}b+1$

Key Points to Remember

Essential concepts to master this topic

Rule: Isolate x by moving all x terms to one side
Technique: Subtract 2x from both sides: 5x - 2x = 3x
Check: Test with specific b value: if b = 6, then x > -1 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to flip the inequality sign when dividing by negative
Don't assume division is always positive when parameters are involved! If you're dividing by a negative coefficient, the inequality sign must flip. Always check if your divisor could be negative and handle accordingly.

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

Why is there a parameter b in my answer?

The parameter b stays in your final answer because it's an unknown constant! Your solution $x > -\frac{1}{3}b + 1$ works for any value of b.

How do I check my answer when b is unknown?

Pick any specific value for b and test it! For example, if b = 3, then $x > -1 + 1 = 0$ . Try x = 1 in the original: 5(1) + 3 > 2(1) + 3 becomes 8 > 5 ✓

What if I get confused with the algebra steps?

Take it slow: First collect like terms (get all x terms together), then isolate the variable. Write each step clearly: 5x + b > 2x + 3 → 3x + b > 3 → 3x > 3 - b → x > (3-b)/3

Does the inequality direction ever change in this problem?

No! We only subtract terms and divide by positive 3, so the inequality direction stays the same throughout. The > symbol never flips to <.

Can I solve this graphically?

Yes! Graph $y = 5x + b$ and $y = 2x + 3$ . The solution is where the first line is above the second line (to the right of their intersection point).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Inequality questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime