Solve the Linear Equation: Find X in 16.8 - 3.5x = 27.3

Q: Why do I subtract 16.8 from both sides instead of adding?

Because 16.8 is positive on the left side, you need to subtract it to cancel it out. The goal is to get $ -3.5x $ by itself, so you do the opposite of what's there.

Q: What if I get confused about positive and negative signs?

Write each step clearly: $ 16.8 - 3.5x - 16.8 = 27.3 - 16.8 $. The 16.8 terms cancel on the left, leaving only $ -3.5x $.

Q: How do I divide by a negative number like -3.5?

Treat it just like regular division! $ \frac{10.5}{-3.5} = -3 $ because positive divided by negative equals negative. Use a calculator if needed.

Q: Why is my answer negative?

The answer is negative because we're dividing a positive number (10.5) by a negative number (-3.5). This always gives a negative result!

Q: How can I check if x = -3 is really correct?

Substitute back: $ 16.8 - 3.5(-3) = 16.8 + 10.5 = 27.3 $ ✓. Both sides equal 27.3, so x = -3 is correct!

Linear Equations with Decimal Coefficients

Find the value of the parameter X

$16.8-3.5x=27.3$

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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

00:22 Let's simplify what we can

00:34 Let's isolate the unknown X and calculate

00:46 Let's simplify what we can

00:52 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

Find the value of the parameter X

$16.8-3.5x=27.3$

Step-by-step solution

To find the value of $x$ , we need to solve the equation $16.8 - 3.5x = 27.3$ .

First, we isolate the term involving $x$ . To do this, subtract 16.8 from both sides of the equation:

$16.8 - 3.5x - 16.8 = 27.3 - 16.8$

This simplifies to:

$-3.5x = 10.5$

Next, we solve for $x$ by dividing both sides by the coefficient of $x$ , which is -3.5:

$x = \frac{10.5}{-3.5}$

Perform the division:

$x = -3$

Therefore, the value of the parameter $x$ is $-3$ .

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move all terms with x to one side first
Division Technique: Divide both sides by coefficient: $\frac{10.5}{-3.5} = -3$
Verification Check: Substitute back: $16.8 - 3.5(-3) = 27.3$ ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting to isolate terms
Don't add 16.8 to both sides when 16.8 is already positive = 44.1 instead of 10.5! This moves terms in the wrong direction. Always do the opposite operation: subtract 16.8 from both sides to isolate -3.5x.

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 16.8 from both sides instead of adding?

Because 16.8 is positive on the left side, you need to subtract it to cancel it out. The goal is to get $-3.5x$ by itself, so you do the opposite of what's there.

What if I get confused about positive and negative signs?

Write each step clearly: $16.8 - 3.5x - 16.8 = 27.3 - 16.8$ . The 16.8 terms cancel on the left, leaving only $-3.5x$ .

How do I divide by a negative number like -3.5?

Treat it just like regular division! $\frac{10.5}{-3.5} = -3$ because positive divided by negative equals negative. Use a calculator if needed.

Why is my answer negative?

The answer is negative because we're dividing a positive number (10.5) by a negative number (-3.5). This always gives a negative result!

How can I check if x = -3 is really correct?

Substitute back: $16.8 - 3.5(-3) = 16.8 + 10.5 = 27.3$ ✓. Both sides equal 27.3, so x = -3 is correct!

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Solve the Linear Equation: Find X in 16.8 - 3.5x = 27.3

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 subtract 16.8 from both sides instead of adding?

What if I get confused about positive and negative signs?

How do I divide by a negative number like -3.5?

Why is my answer negative?

How can I check if x = -3 is really correct?

🌟 Unlock Your Math Potential

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