Solve the Equation: Finding X in -4x = 1 + x

Q: Why subtract x from both sides instead of adding 4x?

Both methods work mathematically! However, subtracting x keeps the coefficient negative (-5x), which is simpler to work with than positive coefficients when you have more negative terms.

Q: How do I remember which direction to move variables?

Think of it as collecting like terms. Move all x terms to the side that already has the most x terms, or choose the side that gives you a simpler coefficient to work with.

Q: What if I get confused with the negative signs?

Write each step clearly: $ -4x - x = 1 + x - x $ becomes $ -5x = 1 $. Take your time with combining like terms and double-check your arithmetic.

Q: Is there a way to avoid fractions in my answer?

Not always! Many linear equations naturally have fractional solutions. Fractions are exact answers - don't convert to decimals unless specifically asked. Always leave fractions in lowest terms.

Q: How can I check if my negative fraction is correct?

Substitute back carefully: $ -4 \times (-\frac{1}{5}) = \frac{4}{5} $ and $ 1 + (-\frac{1}{5}) = \frac{4}{5} $. Both sides equal $ \frac{4}{5} $, so your answer is correct!

Linear Equations with Variable Isolation

Find the value of X

$-4x=1+x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Arrange the equation so that one side contains only the unknown X

00:09 Combine like terms

00:15 Isolate X

00:19 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the value of X

$-4x=1+x$

Step-by-step solution

To solve the equation $-4x = 1 + x$ , let's follow these steps:

Step 1: Subtract $x$ from both sides of the equation to start isolating $x$ . This gives: $-4x - x = 1 + x - x$ .
Step 2: Simplify the equation. Combine like terms: $-5x = 1$ .
Step 3: Divide both sides by $-5$ to solve for $x$ : $x = \frac{1}{-5}$ .

Therefore, the solution to the equation is $x = -\frac{1}{5}$ .

Final Answer

$-\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move all x terms to one side first
Technique: Subtract x from both sides: -4x - x = -5x
Check: Substitute $x = -\frac{1}{5}$ : $-4(-\frac{1}{5}) = \frac{4}{5}$ and $1 + (-\frac{1}{5}) = \frac{4}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding x to both sides instead of subtracting
Don't add x to both sides when you have -4x = 1 + x, giving -3x = 1 + 2x = wrong equation! This moves variables in the wrong direction and creates more complex terms. Always move variables to the same side by subtracting the smaller coefficient.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why subtract x from both sides instead of adding 4x?

Both methods work mathematically! However, subtracting x keeps the coefficient negative (-5x), which is simpler to work with than positive coefficients when you have more negative terms.

How do I remember which direction to move variables?

Think of it as collecting like terms. Move all x terms to the side that already has the most x terms, or choose the side that gives you a simpler coefficient to work with.

What if I get confused with the negative signs?

Write each step clearly: $-4x - x = 1 + x - x$ becomes $-5x = 1$ . Take your time with combining like terms and double-check your arithmetic.

Is there a way to avoid fractions in my answer?

Not always! Many linear equations naturally have fractional solutions. Fractions are exact answers - don't convert to decimals unless specifically asked. Always leave fractions in lowest terms.

How can I check if my negative fraction is correct?

Substitute back carefully: $-4 \times (-\frac{1}{5}) = \frac{4}{5}$ and $1 + (-\frac{1}{5}) = \frac{4}{5}$ . Both sides equal $\frac{4}{5}$ , so your answer is correct!

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