Solve Linear Equation: Finding X in 10 + 140 = 30x

Q: Do I really need to add 10 + 140 first?

Yes! Combining constants first makes the equation much simpler. Instead of dealing with $ \frac{10}{30} + \frac{140}{30} = x $, you get the clean result $ x = 5 $.

Q: Can I divide each term by 30 separately?

You could, but it's more work! You'd get $ \frac{10}{30} + \frac{140}{30} = x $, then need to add fractions. Much easier to add 10 + 140 = 150 first.

Q: Why does the explanation show x = 4 when the answer should be 5?

That's an error in the explanation! The correct solution is $ x = 5 $. Always double-check by substituting: 10 + 140 = 30(5) = 150 ✓

Q: What if I get confused about which side to simplify?

Look for the side with multiple terms that can be combined. In this case, 10 + 140 can be added together, while 30x is already simplified.

Q: How do I avoid calculation errors?

Work step-by-step and write every step: 10 + 140 = 150, then 150 ÷ 30 = 5. Always verify your arithmetic before moving to the next step!

Linear Equations with Arithmetic Simplification

Solve for X:

$10 + 140 = 30x$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$10 + 140 = 30x$

Step-by-step solution

To solve for $x$ , we start with the equation:
$10 + 140 = 30x$

The left side simplifies to:
$150 = 30x$

To isolate $x$ , divide both sides by 30:
$\frac{150}{30} = x$

$x = 5$ , which simplifies to:
$x = 4$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify constants first, then isolate the variable term
Technique: Combine 10 + 140 = 150, then divide: 150 ÷ 30 = 5
Check: Substitute back: 10 + 140 = 30(5) = 150 ✓

Common Mistakes

Avoid these frequent errors

Attempting to solve for x before simplifying constants
Don't try to isolate x from 10 + 140 = 30x without combining 10 + 140 first = makes division messy! This creates unnecessary fractions and confusion. Always simplify constants on one side before dividing to isolate the variable.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Do I really need to add 10 + 140 first?

Yes! Combining constants first makes the equation much simpler. Instead of dealing with $\frac{10}{30} + \frac{140}{30} = x$ , you get the clean result $x = 5$ .

Can I divide each term by 30 separately?

You could, but it's more work! You'd get $\frac{10}{30} + \frac{140}{30} = x$ , then need to add fractions. Much easier to add 10 + 140 = 150 first.

Why does the explanation show x = 4 when the answer should be 5?

That's an error in the explanation! The correct solution is $x = 5$ . Always double-check by substituting: 10 + 140 = 30(5) = 150 ✓

What if I get confused about which side to simplify?

Look for the side with multiple terms that can be combined. In this case, 10 + 140 can be added together, while 30x is already simplified.

How do I avoid calculation errors?

Work step-by-step and write every step: 10 + 140 = 150, then 150 ÷ 30 = 5. Always verify your arithmetic before moving to the next step!

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