Solve for X in the Linear Equation: 3x + 5 = 20

Q: Why do I subtract 5 from both sides first?

You want to isolate the term with x (which is 3x) before dealing with the coefficient. Subtracting 5 first gives you $ 3x = 15 $, which is much simpler than working with fractions!

Q: What if I accidentally add 5 instead of subtracting?

Adding 5 to both sides gives $ 3x + 10 = 25 $, which makes the problem harder! Remember: to undo addition, you must subtract the same number from both sides.

Q: Can I check my answer a different way?

Yes! You can also think about it logically: "What number times 3, plus 5, equals 20?" Since 3 × 5 = 15, and 15 + 5 = 20, the answer is 5.

Q: What if my equation had subtraction instead?

For equations like $ 3x - 5 = 10 $, you'd add 5 to both sides first. The key is using the opposite operation to undo what's being done to x.

Q: Do I always divide last?

When solving $ ax + b = c $ type equations, yes! First handle the constant (b), then divide by the coefficient (a). This order keeps your work clean and simple.

Linear Equations with Isolation Steps

$3x + 5 = 20$

$x = \text{?}$

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Understand the problem

$3x + 5 = 20$

$x = \text{?}$

Step-by-step solution

To solve the equation $3x + 5 = 20$ , follow these steps:

1. Subtract 5 from both sides: $3x = 20 - 5$

2. Simplify the right side: $3x = 15$

3. Divide both sides by 3: $x = \frac{15}{3}$

4. Solve: $x = 5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable term
Technique: Subtract 5 first, then divide: 3x = 15, so x = 5
Check: Substitute back: 3(5) + 5 = 15 + 5 = 20 ✓

Common Mistakes

Avoid these frequent errors

Dividing by the coefficient before removing the constant
Don't divide 3x + 5 = 20 by 3 first = $x + \frac{5}{3} = \frac{20}{3}$ ! This creates messy fractions and makes the problem harder. Always subtract or add constants first, then divide by the coefficient.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I subtract 5 from both sides first?

You want to isolate the term with x (which is 3x) before dealing with the coefficient. Subtracting 5 first gives you $3x = 15$ , which is much simpler than working with fractions!

What if I accidentally add 5 instead of subtracting?

Adding 5 to both sides gives $3x + 10 = 25$ , which makes the problem harder! Remember: to undo addition, you must subtract the same number from both sides.

Can I check my answer a different way?

Yes! You can also think about it logically: "What number times 3, plus 5, equals 20?" Since 3 × 5 = 15, and 15 + 5 = 20, the answer is 5.

What if my equation had subtraction instead?

For equations like $3x - 5 = 10$ , you'd add 5 to both sides first. The key is using the opposite operation to undo what's being done to x.

Do I always divide last?

When solving $ax + b = c$ type equations, yes! First handle the constant (b), then divide by the coefficient (a). This order keeps your work clean and simple.

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