Solve the Linear Equation: 8x + 4 = 4 Step by Step

Q: Why is the answer x = 0 and not just 0?

Great question! $ x = 0 $ tells us the value of the variable x. Just writing 0 doesn't show what equals zero. Always write your answer as variable = value.

Q: What does it mean when x equals zero?

When $ x = 0 $, it means the variable has no quantity - it's neither positive nor negative. This is a perfectly valid solution that many students forget to consider!

Q: How do I know which operation to do first?

Work backwards from the order of operations! Since we added 4 to $ 8x $, we undo it by subtracting 4 first, then divide by 8 to isolate x.

Q: Can linear equations have zero as the answer?

Absolutely! $ x = 0 $ is a common and valid solution for linear equations. Don't assume zero means 'no solution' - it means the variable's value is zero.

Q: What if I divided by 8 first instead?

You'd get $ x + \frac{1}{2} = \frac{1}{2} $, which works but creates fractions unnecessarily. It's usually easier to eliminate constants before dividing by coefficients.

Linear Equations with Zero Solutions

$8x+4=4$

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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.

00:09 First, we need to focus on finding the unknown X.

00:13 We should rearrange the equation. Make sure one side has only the X.

00:19 Next, let's fully isolate the X so we can see its value.

00:23 And there we have it! We've found the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$8x+4=4$

Step-by-step solution

We will solve the given linear equation $8x + 4 = 4$ step-by-step:

Step 1: Subtract 4 from both sides of the equation to begin isolating the variable $x$ :

$8x + 4 - 4 = 4 - 4$

This simplifies to:

$8x = 0$

Step 2: Divide both sides of the equation by 8 to solve for $x$ :

$\frac{8x}{8} = \frac{0}{8}$

This results in:

$x = 0$

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

Final Answer

$x=0$

Key Points to Remember

Essential concepts to master this topic

Isolation: Remove constants by adding or subtracting from both sides
Technique: Subtract 4: $8x + 4 - 4 = 4 - 4$ gives $8x = 0$
Check: Substitute back: $8(0) + 4 = 0 + 4 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to perform the same operation on both sides
Don't subtract 4 from only one side = unbalanced equation! This violates the fundamental rule of equations and gives completely wrong answers. Always perform identical operations on both sides 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 is the answer x = 0 and not just 0?

Great question! $x = 0$ tells us the value of the variable x. Just writing 0 doesn't show what equals zero. Always write your answer as variable = value.

What does it mean when x equals zero?

When $x = 0$ , it means the variable has no quantity - it's neither positive nor negative. This is a perfectly valid solution that many students forget to consider!

How do I know which operation to do first?

Work backwards from the order of operations! Since we added 4 to $8x$ , we undo it by subtracting 4 first, then divide by 8 to isolate x.

Can linear equations have zero as the answer?

Absolutely! $x = 0$ is a common and valid solution for linear equations. Don't assume zero means 'no solution' - it means the variable's value is zero.

What if I divided by 8 first instead?

You'd get $x + \frac{1}{2} = \frac{1}{2}$ , which works but creates fractions unnecessarily. It's usually easier to eliminate constants before dividing by coefficients.

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