Solve for X in the Linear Equation 3x = 18

Q: Why do I divide both sides by 3?

You divide both sides by 3 because that's the coefficient of x. This isolates x on one side while keeping the equation balanced - whatever you do to one side, you must do to the other!

Q: How do I check if x = 6 is correct?

Substitute x = 6 back into the original equation: $ 3(6) = 18 $. Since 18 = 18, your answer is correct!

Q: What if I get a fraction as my answer?

That's perfectly normal! For example, if you had $ 3x = 5 $, then $ x = \frac{5}{3} $. Always simplify fractions and check your work.

Linear Equations with Division Method

Solve for X:

$3x=18$

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Understand the problem

Solve for X:

$3x=18$

Step-by-step solution

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3.

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

Then divide accordingly:

$x=6$

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Division Rule: To isolate x, divide both sides by the coefficient
Technique: Divide 18 by 3 to get x = 6
Check: Substitute back: 3(6) = 18 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Dividing only one side of the equation
Don't divide just 3x by 3 and leave 18 unchanged = x = 18 which is wrong! This breaks the balance of the equation. Always divide both sides by the same number to maintain equality.

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 divide both sides by 3?

You divide both sides by 3 because that's the coefficient of x. This isolates x on one side while keeping the equation balanced - whatever you do to one side, you must do to the other!

What if the coefficient was negative, like -3x = 18?

You still divide both sides by the coefficient! Divide both sides by -3 to get $x = \frac{18}{-3} = -6$ .

Can I multiply instead of divide?

Yes! Instead of dividing by 3, you can multiply both sides by $\frac{1}{3}$ . Both methods give the same result: x = 6.

How do I check if x = 6 is correct?

Substitute x = 6 back into the original equation: $3(6) = 18$ . Since 18 = 18, your answer is correct!

What if I get a fraction as my answer?

That's perfectly normal! For example, if you had $3x = 5$ , then $x = \frac{5}{3}$ . Always simplify fractions and check your work.

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