Solve the Linear Equation 6x = 72 for X

Q: Why do I divide both sides by 6?

You need to isolate x by getting rid of the 6 multiplying it. Division is the opposite operation of multiplication, so dividing both sides by 6 cancels out the coefficient.

Q: What if I subtract 6 from both sides instead?

That won't work! Since 6 is multiplied by x (not added), you need to use division to undo it. Subtraction only works when numbers are added or subtracted from x.

Q: How do I check if x = 12 is correct?

Substitute 12 back into the original equation: $ 6(12) = 72 $. Since 72 = 72 is true, your answer is correct!

Q: What if the coefficient was negative, like -6x = 72?

Same process! Divide both sides by -6: $ x = \frac{72}{-6} = -12 $. The sign of the coefficient affects your final answer.

Q: Can I multiply both sides by 1/6 instead of dividing by 6?

Yes! Multiplying by $ \frac{1}{6} $ gives the same result as dividing by 6. Both methods work because division and multiplication by reciprocals are equivalent.

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

00:10 Let's arrange the equation so that one side has only the unknown X

00:18 Let's reduce what we can

00:22 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 for X:

$6x=72$

2

Step-by-step solution

To solve for $x$ in the equation $6x = 72$ , follow these steps:

Step 1: Identify the equation and the coefficient of $x$ .
The given equation is $6x = 72$ , where the coefficient of $x$ is 6.

Step 2: Isolate $x$ by dividing both sides of the equation by the coefficient (6).
Perform the division: $x = \frac{72}{6}$ .

Step 3: Simplify the result.
Calculating $\frac{72}{6}$ , we get $x = 12$ .

Therefore, the solution to the equation is $x = 12$ .

3

Final Answer

12

Key Points to Remember

Essential concepts to master this topic

Division Rule: Divide both sides by the coefficient of x
Technique: $\frac{72}{6} = 12$ isolates the variable completely
Check: Substitute back: $6(12) = 72$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Dividing only one side of the equation
Don't divide just the left side by 6 leaving 72 unchanged = x = 72 instead of 12! This breaks the equality because you must perform the same operation on both sides. Always divide both sides by the coefficient.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I divide both sides by 6?

+

You need to isolate x by getting rid of the 6 multiplying it. Division is the opposite operation of multiplication, so dividing both sides by 6 cancels out the coefficient.

What if I subtract 6 from both sides instead?

+

That won't work! Since 6 is multiplied by x (not added), you need to use division to undo it. Subtraction only works when numbers are added or subtracted from x.

How do I check if x = 12 is correct?

+

Substitute 12 back into the original equation: $6(12) = 72$ . Since 72 = 72 is true, your answer is correct!

What if the coefficient was negative, like -6x = 72?

+

Same process! Divide both sides by -6: $x = \frac{72}{-6} = -12$ . The sign of the coefficient affects your final answer.

Can I multiply both sides by 1/6 instead of dividing by 6?

+

Yes! Multiplying by $\frac{1}{6}$ gives the same result as dividing by 6. Both methods work because division and multiplication by reciprocals are equivalent.

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Solve the Linear Equation 6x = 72 for X

Linear Equations with Integer Coefficients

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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 divide both sides by 6?

What if I subtract 6 from both sides instead?

How do I check if x = 12 is correct?

What if the coefficient was negative, like -6x = 72?

Can I multiply both sides by 1/6 instead of dividing by 6?

🌟 Unlock Your Math Potential

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