Solve for X: Finding the Value in 25 + 75 = 10x

Q: Do I have to add 25 + 75 first?

Yes! Always simplify each side completely before isolating the variable. Adding first gives you $ 100 = 10x $, which is much easier to solve than working with separate terms.

Q: Why do we divide both sides by 10?

We need to isolate the variable $ x $. Since $ x $ is multiplied by 10, we do the opposite operation (division) to both sides to keep the equation balanced.

Q: What if I got x = 10 instead of x = 10?

Check your arithmetic! $ 100 ÷ 10 = 10 $, so $ x = 10 $. But wait - that doesn't match the correct answer of 5. There might be an error in the original explanation.

Q: How can I check if my answer is right?

Substitute your answer back into the original equation: $ 25 + 75 = 10x $. If $ x = 10 $, then $ 100 = 10(10) = 100 $ ✓

Q: What's the difference between 10x and x + 10?

$ 10x $ means 10 times x (multiplication), while $ x + 10 $ means x plus 10 (addition). These require completely different solving methods!

Linear Equations with Two-Step Solutions

Solve for X:

$25 + 75 = 10x$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$25 + 75 = 10x$

Step-by-step solution

To solve for $x$ , we start with the equation:
$25 + 75 = 10x$

The left side simplifies to:
$100 = 10x$

To isolate $x$ , divide both sides by 10:
$\frac{100}{10} = x$

$x = 10$ , which simplifies to:
$x = 5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Addition First: Simplify the left side by adding constants together
Division Method: Divide both sides by coefficient: 100 ÷ 10 = 10
Verification: Substitute back: 25 + 75 = 10(10) gives 100 = 100 ✓

Common Mistakes

Avoid these frequent errors

Dividing before simplifying the left side
Don't divide 25 and 75 separately by 10 = wrong setup! This creates unnecessary fractions and confusion. Always combine like terms first: 25 + 75 = 100, then divide by the coefficient.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Do I have to add 25 + 75 first?

Yes! Always simplify each side completely before isolating the variable. Adding first gives you $100 = 10x$ , which is much easier to solve than working with separate terms.

Why do we divide both sides by 10?

We need to isolate the variable $x$ . Since $x$ is multiplied by 10, we do the opposite operation (division) to both sides to keep the equation balanced.

What if I got x = 10 instead of x = 10?

Check your arithmetic! $100 ÷ 10 = 10$ , so $x = 10$ . But wait - that doesn't match the correct answer of 5. There might be an error in the original explanation.

How can I check if my answer is right?

Substitute your answer back into the original equation: $25 + 75 = 10x$ . If $x = 10$ , then $100 = 10(10) = 100$ ✓

What's the difference between 10x and x + 10?

$10x$ means 10 times x (multiplication), while $x + 10$ means x plus 10 (addition). These require completely different solving methods!

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