Solving Linear Equation: Finding X in 5.214 - 3.24X = -4.51

Linear Equations with Decimal Coefficients

Solve for X:

5.2143.24x=4.51 5.214-3.24x=-4.51

❤️ 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
00:00 Solve
00:03 We want to isolate the unknown X
00:08 Let's arrange the equation so that one side has only the unknown X
00:28 Let's simplify what we can
00:41 Let's isolate the unknown X and calculate
00:52 Let's simplify what we can
00:59 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

5.2143.24x=4.51 5.214-3.24x=-4.51

2

Step-by-step solution

To solve the equation 5.2143.24x=4.515.214 - 3.24x = -4.51, we begin by isolating the term with the variable.

  • Step 1: Move the constant term on the left side to the right side of the equation. Subtract 5.214 from both sides:

5.2143.24x5.214=4.515.214 5.214 - 3.24x - 5.214 = -4.51 - 5.214

This simplifies to:

3.24x=9.724 -3.24x = -9.724
  • Step 2: Solve for xx by dividing both sides by the coefficient of xx, which is -3.24:

x=9.7243.24 x = \frac{-9.724}{-3.24}

Perform the division:

x=3.001 x = 3.001

Thus, the solution to the equation is x=3.001 x = 3.001 , aligning with the correct choice given the options.

3

Final Answer

3.001

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Move constants to one side, variables to the other
  • Technique: Subtract 5.214 from both sides: -3.24x = -9.724
  • Check: Substitute x = 3.001: 5.214 - 3.24(3.001) = -4.51 ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting when moving terms
    Don't add 5.214 to both sides when moving it from left to right = wrong answer like x = 0.25! This keeps the constant on the wrong side. Always do the opposite operation: if it's +5.214, subtract 5.214 from both sides.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why do I subtract 5.214 instead of adding it?

+

When moving a term across the equals sign, you do the opposite operation. Since 5.214 is being added on the left side, you subtract it from both sides to cancel it out.

How do I handle the negative signs when dividing?

+

Remember: negative divided by negative equals positive! So 9.7243.24=+3.001 \frac{-9.724}{-3.24} = +3.001 . The negatives cancel out.

What if I get a different decimal answer?

+

Double-check your arithmetic! Common errors include wrong subtraction (5.214 - (-4.51)) or incorrect division. Use a calculator if needed and always verify your answer.

Can I solve this by moving the x term first instead?

+

Yes! You could add 3.24x 3.24x to both sides first, then subtract constants. Either order works as long as you do the same operation to both sides.

How precise should my final answer be?

+

Match the precision given in the problem. Since the coefficients have 3 decimal places, your answer should typically have 3 decimal places too: x = 3.001.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) 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