Solve the Linear Equation: 7.21 + 11.5x - 3.4x = 8.11x - 12.4 + 3.8

Q: Why is my final answer such a large number like 1581?

Large answers are normal when you have small coefficients like 0.01x! When you divide by a small decimal (0.01), you get a much larger result. Think: $ \frac{15.81}{0.01} = 1581 $

Q: How do I avoid arithmetic mistakes with decimals?

Line up decimal points when adding/subtracting and double-check each step. For example: 11.5 - 3.4 = 8.1, not 7.1!

Q: Should I move x terms to the left or right side?

Either works! The key is to be consistent. In this problem, moving x terms to the right gives 0.01x, which is easier to work with than -0.01x.

Q: How can I check such a big answer quickly?

Use the distributive property strategically! Calculate $ 8.1 \times 1581 $ and $ 8.11 \times 1581 $ separately, then verify both sides equal the same value.

Linear Equations with Decimal Coefficients

Solve for X:

$7.21+11.5x-3.4x=8.11x-12.4+3.8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:05 Group like terms

00:18 Arrange the equation so that X is isolated on one side

00:36 Group like terms

00:48 Isolate X

00:56 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$7.21+11.5x-3.4x=8.11x-12.4+3.8$

Step-by-step solution

To solve this problem, let's carefully simplify and solve the given equation:

Step 1: Simplify each side of the equation.
Left side: $7.21 + 11.5x - 3.4x$ which simplifies to $7.21 + (11.5 - 3.4)x = 7.21 + 8.1x$ .
Right side: $8.11x - 12.4 + 3.8$ which simplifies to $8.11x - 8.6$ .
Step 2: Set up the simplified equation.
We have $7.21 + 8.1x = 8.11x - 8.6$ .
Step 3: Move terms involving $x$ to one side and constants to the other.
Subtract $8.1x$ from both sides: $7.21 = 8.11x - 8.6 - 8.1x$ .
This simplifies to $7.21 = 0.01x - 8.6$ .
Step 4: Solve for $x$ .
Add $8.6$ to both sides to isolate terms with $x$ : $7.21 + 8.6 = 0.01x$ , which simplifies to $15.81 = 0.01x$ .
Divide both sides by 0.01 to solve for $x$ :
$x = \frac{15.81}{0.01} = 1581$ .

Therefore, the solution to the problem is $x = 1581$ .

Final Answer

$1581$

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine like terms on each side first
Technique: Move all x terms to one side: 8.1x - 8.11x = -0.01x
Check: Substitute x = 1581: 7.21 + 8.1(1581) = 8.11(1581) - 8.6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms correctly
Don't skip combining 11.5x - 3.4x = 7.1x instead of 8.1x! This calculation error leads to completely wrong coefficients and final answers. Always double-check your arithmetic when combining decimal coefficients.

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 is my final answer such a large number like 1581?

Large answers are normal when you have small coefficients like 0.01x! When you divide by a small decimal (0.01), you get a much larger result. Think: $\frac{15.81}{0.01} = 1581$

How do I avoid arithmetic mistakes with decimals?

Line up decimal points when adding/subtracting and double-check each step. For example: 11.5 - 3.4 = 8.1, not 7.1!

Should I move x terms to the left or right side?

Either works! The key is to be consistent. In this problem, moving x terms to the right gives 0.01x, which is easier to work with than -0.01x.

What if I get a negative coefficient for x?

No problem! Just divide by the negative number. For example, if you have $-0.01x = 15.81$ , then $x = \frac{15.81}{-0.01} = -1581$ .

How can I check such a big answer quickly?

Use the distributive property strategically! Calculate $8.1 \times 1581$ and $8.11 \times 1581$ separately, then verify both sides equal the same value.

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Solve the Linear Equation: 7.21 + 11.5x - 3.4x = 8.11x - 12.4 + 3.8

Linear Equations with Decimal Coefficients

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is my final answer such a large number like 1581?

How do I avoid arithmetic mistakes with decimals?

Should I move x terms to the left or right side?

What if I get a negative coefficient for x?

How can I check such a big answer quickly?

🌟 Unlock Your Math Potential

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