Find X in the Linear Equation: 7.24x - 3.5 = 6.21

Linear Equations with Decimal Coefficients

Find the value of the parameter X

7.24x3.5=6.21 7.24x-3.5=6.21

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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
00:07 Let's arrange the equation so that one side has only the unknown X
00:19 Let's simplify what we can
00:31 Let's isolate the unknown X, and calculate
00:49 Let's simplify what we can
00:55 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the value of the parameter X

7.24x3.5=6.21 7.24x-3.5=6.21

2

Step-by-step solution

To solve the linear equation 7.24x3.5=6.21 7.24x - 3.5 = 6.21 , we will apply the following steps:

  • Step 1: Add 3.5 to both sides of the equation to isolate the term containing x x .
  • Step 2: Perform the addition on the right side to simplify the expression.
  • Step 3: Divide both sides by 7.24 to solve for x x .
  • Step 4: Calculate the division to obtain the value of x x .

Let's execute these steps one by one:

Step 1: Add 3.5 to both sides:

7.24x3.5+3.5=6.21+3.5 7.24x - 3.5 + 3.5 = 6.21 + 3.5

This simplifies to:

7.24x=9.71 7.24x = 9.71

Step 2: Divide both sides by 7.24 to solve for x x :

x=9.717.24 x = \frac{9.71}{7.24}

Step 3: Calculate the division:

x1.34 x \approx 1.34

Therefore, the solution to the problem is x=1.34 x = 1.34 , which corresponds to Choice 3.

3

Final Answer

1.34

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Add or subtract to move constants to one side
  • Technique: Add 3.5 to both sides: 6.21 + 3.5 = 9.71
  • Check: Substitute back: 7.24(1.34) - 3.5 = 6.21 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to perform operations on both sides
    Don't add 3.5 to only the left side = unbalanced equation giving wrong answer! This violates the fundamental property of equality. Always perform the same operation on both sides of the equation.

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 need to add 3.5 to both sides instead of just one side?

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An equation is like a balanced scale. If you add weight to only one side, it tips over! You must maintain the balance by doing the same thing to both sides.

How do I handle decimals when dividing?

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When dividing decimals like 9.717.24 \frac{9.71}{7.24} , use long division or a calculator. Round carefully - here we get approximately 1.34.

What if I get a slightly different decimal answer?

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Small differences in the last decimal place are normal due to rounding. Always check which answer choice is closest to your calculated result.

Can I move the x term to the right side instead?

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Yes! You could subtract 7.24x 7.24x from both sides to get 3.5=6.217.24x -3.5 = 6.21 - 7.24x . Just remember to keep track of signs when rearranging.

How do I check my answer without a calculator?

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Substitute your answer back: 7.24(1.34)3.5 7.24(1.34) - 3.5 . You can estimate: 7×1.3=9.1 7 \times 1.3 = 9.1 , then 9.13.55.6 9.1 - 3.5 ≈ 5.6 , which is close to 6.21!

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