Solve the Linear Inequality: 8x+a < 3x-4 | Step-by-Step Solution

Linear Inequalities with Parameter Variables

Solve the inequality:

8x+a<3x4 8x+a < 3x-4

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the inequality:

8x+a<3x4 8x+a < 3x-4

2

Step-by-step solution

Solving an inequality equation is just like a normal equation. We start by trying to isolate the variable (X).

It is important to note that in this equation there are two variables (X and a), so we may not reach a final result.

8x+a<3x-4

We move the sections

8x-3x<-4-a

We reduce the terms

5x<-4-a

We divide by 5

x< -a/5 -4/5

And this is the solution!

3

Final Answer

x<15a45 x < -\frac{1}{5}a-\frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Treat parameters like constants when isolating the main variable
  • Technique: Move terms: 8x - 3x < -4 - a becomes 5x < -4 - a
  • Check: Substitute back: if x = -1, then 8(-1) + a should be less than 3(-1) - 4 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing by a negative coefficient without flipping the inequality sign
    Don't divide 5x < -4 - a by 5 and keep the same inequality direction = wrong solution! When dividing by positive numbers, the inequality stays the same. Always divide by the coefficient carefully: since 5 is positive, x < (-4 - a)/5.

Practice Quiz

Test your knowledge with interactive questions

Solve the inequality:


\( 5-3x>-10 \)

FAQ

Everything you need to know about this question

Why does my answer have both x and a in it?

+

This is normal! Since a is a parameter (unknown constant), your final answer will express x in terms of a. The solution x<a545 x < -\frac{a}{5} - \frac{4}{5} is complete.

How do I check my answer when there are two variables?

+

Pick any value for a, then choose an x value that satisfies your inequality. Substitute both into the original inequality to verify both sides work out correctly.

What does the fraction -4/5 mean in my answer?

+

The fraction 45 -\frac{4}{5} comes from dividing -4 by 5. This is the constant part of your solution, separate from the part that depends on parameter a.

Why is the inequality sign < and not ≤?

+

The original problem uses strict inequality (<) meaning "less than" not "less than or equal to". When you solve the inequality, you must preserve this - so the answer keeps the < sign.

Can I solve this if a has a specific number?

+

Yes! If you're told a = 2 for example, substitute it in: x<2545=65 x < -\frac{2}{5} - \frac{4}{5} = -\frac{6}{5} . The parameter solution works for any value of a.

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations