Solve the Linear Equation: Finding X in 5x = 0

Linear Equations with Zero Product

5x=0 5x=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem step by step.
00:08 First, we'll isolate the unknown, X. Let's do it together.
00:15 Next, let's simplify what we can. You're doing great!
00:19 Remember, zero divided by any number is always, zero.
00:25 And that's how we find the solution. Excellent job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5x=0 5x=0

2

Step-by-step solution

To solve the equation 5x=0 5x = 0 for x x , we will use the following steps:

  • Step 1: Identify that the equation is 5x=0 5x = 0 .
  • Step 2: To solve for x x , divide both sides of the equation by 5.

Let's perform the calculation as outlined in Step 2:

5x=0 5x = 0

Divide both sides by 5 to isolate x x :

x=05 x = \frac{0}{5}

Simplifying, this gives:

x=0 x = 0

Therefore, the solution to the equation 5x=0 5x = 0 is x=0 x = 0 .

The correct answer is option 4: x=0 x = 0 .

3

Final Answer

x=0 x=0

Key Points to Remember

Essential concepts to master this topic
  • Zero Property: Any number multiplied by zero equals zero
  • Division Method: Divide both sides by 5 to get x=05=0 x = \frac{0}{5} = 0
  • Verification: Substitute back into original equation: 5(0)=0 5(0) = 0

Common Mistakes

Avoid these frequent errors
  • Thinking the answer is 5 or 1/5
    Don't divide 5 by 0 or find reciprocals = undefined or wrong answer! This ignores the zero on the right side. Always isolate x by dividing both sides by the coefficient: x=05=0 x = \frac{0}{5} = 0 .

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 isn't the answer x = 5?

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Remember, we need to isolate x, not find what multiplies with it. We divide both sides by 5: 5x5=05 \frac{5x}{5} = \frac{0}{5} , which gives us x=0 x = 0 .

Can I just ignore the 5 in front of x?

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Never ignore coefficients! The 5 tells us that x is multiplied by 5. To undo multiplication, we must divide both sides by that same number.

What does it mean when x equals zero?

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When x=0 x = 0 , it means the variable has a value of zero. This is a perfectly valid solution - zero is a real number just like any other!

How do I check if x = 0 is correct?

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Substitute x=0 x = 0 back into the original equation: 5(0)=0 5(0) = 0 . Since 0=0 0 = 0 is true, our answer is correct!

Why do we get zero divided by five?

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When we divide both sides by 5, we get x=05 x = \frac{0}{5} . Since zero divided by any non-zero number equals zero, this simplifies to x=0 x = 0 .

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