Solve the Equation with Decimals: 27.213 + 5.21x = 28.32

Q: Why do I need to subtract 27.213 from both sides first?

You need to isolate the variable term 5.21x by itself! Subtracting 27.213 from both sides removes it from the left side while keeping the equation balanced.

Q: How do I divide 1.107 by 5.21 without a calculator?

You can use long division with decimals or convert to fractions first. Move decimal points to make 5.21 into 521, then divide 110.7 ÷ 521 = 0.212.

Q: What if I get a different decimal when dividing?

Double-check your subtraction first! Make sure you got $ 28.32 - 27.213 = 1.107 $. Then carefully divide, rounding only at the very end if needed.

Q: How can I verify my answer is correct?

Substitute x = 0.212 back into the original equation: $ 27.213 + 5.21(0.212) $. Calculate $ 5.21 × 0.212 = 1.10452 $, then $ 27.213 + 1.10452 = 28.31752 ≈ 28.32 $ ✓

Q: Why is my answer slightly different when I check?

This happens due to rounding in decimal calculations. As long as your check gets very close to 28.32 (within 0.01), your answer of 0.212 is correct!

Linear Equations with Decimal Coefficients

Solve for X:

$27.213+5.21x=28.32$

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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

00:08 Let's arrange the equation so that one side has only the unknown X

00:27 Let's simplify what we can

00:38 Let's isolate the unknown X and calculate

00:57 Let's simplify what we can

01:01 And 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:

$27.213+5.21x=28.32$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Isolate the terms involving $x$ .
Step 2: Solve for $x$ by dividing.

Let's proceed with each step:

Step 1: Isolate the terms involving $x$ .
Subtract 27.213 from both sides of the equation:
$27.213 + 5.21x - 27.213 = 28.32 - 27.213$ .

This simplifies to:
$5.21x = 1.107$ .

Step 2: Solve for $x$ by dividing both sides by 5.21:
$x = \frac{1.107}{5.21}$ .

Perform the division:
$x = 0.212$ .

Therefore, the solution to the problem is $x = 0.212$ .

Final Answer

0.212

Key Points to Remember

Essential concepts to master this topic

Isolation: Subtract constants first to isolate the variable term
Technique: Divide by coefficient: $x = \frac{1.107}{5.21} = 0.212$
Check: Substitute back: $27.213 + 5.21(0.212) = 28.32$ ✓

Common Mistakes

Avoid these frequent errors

Making decimal calculation errors when subtracting
Don't rush through 28.32 - 27.213 = 1.117 instead of 1.107! This gives x = 0.214 instead of 0.212. Always line up decimal places carefully and double-check your arithmetic with decimals.

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 subtract 27.213 from both sides first?

You need to isolate the variable term 5.21x by itself! Subtracting 27.213 from both sides removes it from the left side while keeping the equation balanced.

How do I divide 1.107 by 5.21 without a calculator?

You can use long division with decimals or convert to fractions first. Move decimal points to make 5.21 into 521, then divide 110.7 ÷ 521 = 0.212.

What if I get a different decimal when dividing?

Double-check your subtraction first! Make sure you got $28.32 - 27.213 = 1.107$ . Then carefully divide, rounding only at the very end if needed.

How can I verify my answer is correct?

Substitute x = 0.212 back into the original equation: $27.213 + 5.21(0.212)$ . Calculate $5.21 × 0.212 = 1.10452$ , then $27.213 + 1.10452 = 28.31752 ≈ 28.32$ ✓

Why is my answer slightly different when I check?

This happens due to rounding in decimal calculations. As long as your check gets very close to 28.32 (within 0.01), your answer of 0.212 is correct!

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Solve the Equation with Decimals: 27.213 + 5.21x = 28.32

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 do I need to subtract 27.213 from both sides first?

How do I divide 1.107 by 5.21 without a calculator?

What if I get a different decimal when dividing?

How can I verify my answer is correct?

Why is my answer slightly different when I check?

🌟 Unlock Your Math Potential

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