Solve for X: -8x + 1/4 - 3 = -8x Linear Equation

Q: What does 'no solution' actually mean?

No solution means there is no value of x that makes the equation true. The equation is inconsistent - it's asking for something impossible!

Q: How is this different from x = 0?

x = 0 is a specific solution where zero makes the equation work. No solution means no number (including zero) can satisfy the equation.

Q: Why do the x-terms cancel out completely?

Both sides have identical x-terms ($ -8x $). When you subtract them, they eliminate each other, leaving only the constant terms to compare.

Q: Could I have made a mistake in my algebra?

Double-check by verifying each step: $ \frac{1}{4} - 3 = \frac{1}{4} - \frac{12}{4} = -\frac{11}{4} $. If your algebra is correct and you get a false statement, the equation truly has no solution!

Q: What should I write as my final answer?

Write "No solution" or "There is no solution". Some teachers also accept the symbol ∅ (empty set) or "inconsistent equation."

Linear Equations with No Solution

Solve for x:

$-8x+\frac{1}{4}-3=0-8x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find X together.

00:10 First, gather all the like terms.

00:21 Next, arrange the equation to isolate X on one side.

00:31 Then, collect like terms again.

00:35 Oops! We ended up with an illogical expression. So, there's no solution to this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$-8x+\frac{1}{4}-3=0-8x$

Step-by-step solution

We will begin by simplifying both sides of the given equation:

Given: $-8x + \frac{1}{4} - 3 = 0 - 8x$ .

Simplify the left side: Combine the constant terms.

We have $-8x + \frac{1}{4} - 3$ . Converting $-3$ to quarters, we get $-3 = -\frac{12}{4}$ . Thus, combine:

$-8x + \frac{1}{4} - \frac{12}{4} = -8x - \frac{11}{4}$ .

The right side remains as $0 - 8x = -8x$ .
Now, the equation is:

$-8x - \frac{11}{4} = -8x$ .

Next, subtract $-8x$ from both sides to simplify:

$-\frac{11}{4} = 0$ .

This leads to a contradiction since $-\frac{11}{4}$ is not equal to $0$ .

Therefore, the equation has no solution for $x$ .

Hence, the correct answer is There is no solution.

Final Answer

There is no solution.

Key Points to Remember

Essential concepts to master this topic

Rule: When variables cancel out, examine remaining constant statement
Technique: Subtract -8x from both sides: $-\frac{11}{4} = 0$
Check: False statement means no solution exists for any x value ✓

Common Mistakes

Avoid these frequent errors

Thinking you made an algebra error when variables disappear
Don't assume you did something wrong when all x-terms cancel out = you keep trying to find x! This wastes time and creates confusion. Always examine the remaining statement: if it's false like $-\frac{11}{4} = 0$ , then no solution exists.

Practice Quiz

Test your knowledge with interactive questions

$$ -16+a=-17 $$

FAQ

Everything you need to know about this question

What does 'no solution' actually mean?

No solution means there is no value of x that makes the equation true. The equation is inconsistent - it's asking for something impossible!

How is this different from x = 0?

x = 0 is a specific solution where zero makes the equation work. No solution means no number (including zero) can satisfy the equation.

Why do the x-terms cancel out completely?

Both sides have identical x-terms ( $-8x$ ). When you subtract them, they eliminate each other, leaving only the constant terms to compare.

Could I have made a mistake in my algebra?

Double-check by verifying each step: $\frac{1}{4} - 3 = \frac{1}{4} - \frac{12}{4} = -\frac{11}{4}$ . If your algebra is correct and you get a false statement, the equation truly has no solution!

What should I write as my final answer?

Write "No solution" or "There is no solution". Some teachers also accept the symbol ∅ (empty set) or "inconsistent equation."

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