Solve the Algebraic Equation: Determining X in 6x = 3

Q: Why do I divide by 6 instead of multiply?

Since we have 6x = 3, the 6 is multiplied by x. To undo multiplication, we use the opposite operation - division. This isolates x on one side.

Q: Can I get a fraction as my answer?

Absolutely! $ x = \frac{1}{2} $ is a perfectly valid solution. Many linear equations have fractional answers. Just make sure to simplify the fraction if possible.

Q: How do I check if 1/2 is correct?

Substitute $ x = \frac{1}{2} $ back into the original equation: $ 6 \times \frac{1}{2} = 3 $. Since this equals 3, our answer is correct!

Q: What if I forget to simplify 3/6?

Your answer would be $ \frac{3}{6} $ instead of $ \frac{1}{2} $. While mathematically equivalent, always simplify fractions to their lowest terms for the cleanest answer.

Q: Is there another way to solve this?

You could also think of it as "what number times 6 equals 3?" This gives the same answer: $ \frac{1}{2} $. Division is just the most systematic approach.

Linear Equations with Division Method

Solve for X:

$6x=3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve the equation.

00:06 First, we need to isolate the unknown, X.

00:10 Now, arrange the equation so that one side has only X.

00:17 Next, let's simplify what we can.

00:22 We'll factor 6 into 3 and 2.

00:27 Simplify once more.

00:33 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$6x=3$

Step-by-step solution

To solve the equation $6x = 3$ , follow these steps:

Step 1: We aim to isolate $x$ . Divide both sides of the equation by 6 to remove the coefficient attached to $x$ :

x = \frac{3}{6}

Step 2: Simplify the fraction on the right side:

x = \frac{1}{2}

Therefore, the solution to the equation $6x = 3$ is $x = \frac{1}{2}$ .

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Divide both sides by coefficient to isolate variable
Technique: For 6x = 3, divide: x = 3 ÷ 6
Check: Substitute back: 6(1/2) = 3 equals 3 ✓

Common Mistakes

Avoid these frequent errors

Dividing only the coefficient and not both sides
Don't just change 6x to x without dividing 3 by 6 too = wrong equation! This breaks the balance and gives x = 3 instead of 1/2. Always divide both sides by the same number.

Practice Quiz

Test your knowledge with interactive questions

$\frac{-y}{5}=-25$

FAQ

Everything you need to know about this question

Why do I divide by 6 instead of multiply?

Since we have 6x = 3, the 6 is multiplied by x. To undo multiplication, we use the opposite operation - division. This isolates x on one side.

Can I get a fraction as my answer?

Absolutely! $x = \frac{1}{2}$ is a perfectly valid solution. Many linear equations have fractional answers. Just make sure to simplify the fraction if possible.

How do I check if 1/2 is correct?

Substitute $x = \frac{1}{2}$ back into the original equation: $6 \times \frac{1}{2} = 3$ . Since this equals 3, our answer is correct!

What if I forget to simplify 3/6?

Your answer would be $\frac{3}{6}$ instead of $\frac{1}{2}$ . While mathematically equivalent, always simplify fractions to their lowest terms for the cleanest answer.

Is there another way to solve this?

You could also think of it as "what number times 6 equals 3?" This gives the same answer: $\frac{1}{2}$ . Division is just the most systematic approach.

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