Solve the Linear Equation: Finding X in 5x-15=30

Q: Why do I add 15 when the equation shows -15?

You're using inverse operations to isolate x! Since the equation has -15, you add +15 to both sides to cancel it out. Think of it as 'undoing' the subtraction.

Q: Can I divide by 5 first instead of adding 15?

Technically yes, but it creates fractions: $ x - 3 = 6 $. It's usually easier to eliminate constants first, then divide, to avoid working with fractions.

Q: How do I know which operation to do first?

Follow reverse order of operations! Since multiplication and division happen before addition and subtraction, undo addition/subtraction first, then multiplication/division.

Q: What if I get a different answer like x = 3?

Always check your work by substituting back! If x = 3: $ 5(3) - 15 = 15 - 15 = 0 $, not 30. This means you made an error in your steps.

Q: Is there a shortcut for this type of problem?

The pattern is always the same: add/subtract to isolate the variable term, then divide. Once you practice, you can do $ 5x - 15 = 30 $ → $ 5x = 45 $ → $ x = 9 $ quickly!

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

00:07 Let's arrange the equation so that one side has only the unknown X

00:21 Let's group terms

00:28 Let's isolate the unknown X and calculate

00:43 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve the equation

$5x-15=30$

2

Step-by-step solution

We start by moving the sections:

5X-15 = 30
5X = 30+15

5X = 45

Now we divide by 5

X = 9

3

Final Answer

$x=9$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move constants to opposite side using inverse operations
Technique: Add 15 to both sides: 30 + 15 = 45
Check: Substitute back: 5(9) - 15 = 45 - 15 = 30 ✓

Common Mistakes

Avoid these frequent errors

Subtracting 15 from both sides instead of adding
Don't subtract 15 from both sides when you see -15 = wrong direction! This gives 5x = 15, so x = 3, but 5(3) - 15 = 0 ≠ 30. Always do the opposite operation: since we have -15, add 15 to both sides.

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 add 15 when the equation shows -15?

+

You're using inverse operations to isolate x! Since the equation has -15, you add +15 to both sides to cancel it out. Think of it as 'undoing' the subtraction.

Can I divide by 5 first instead of adding 15?

+

Technically yes, but it creates fractions: $x - 3 = 6$ . It's usually easier to eliminate constants first, then divide, to avoid working with fractions.

How do I know which operation to do first?

+

Follow reverse order of operations! Since multiplication and division happen before addition and subtraction, undo addition/subtraction first, then multiplication/division.

What if I get a different answer like x = 3?

+

Always check your work by substituting back! If x = 3: $5(3) - 15 = 15 - 15 = 0$ , not 30. This means you made an error in your steps.

Is there a shortcut for this type of problem?

+

The pattern is always the same: add/subtract to isolate the variable term, then divide. Once you practice, you can do $5x - 15 = 30$ → $5x = 45$ → $x = 9$ quickly!

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Solve the Linear Equation: Finding X in 5x-15=30

Linear Equations with Addition Step

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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 add 15 when the equation shows -15?

Can I divide by 5 first instead of adding 15?

How do I know which operation to do first?

What if I get a different answer like x = 3?

Is there a shortcut for this type of problem?

🌟 Unlock Your Math Potential

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