Solve Linear Equation: Finding X in 8x - 1 = 7x + 5

Q: Which side should I move the x terms to?

Move terms to whichever side gives you a positive coefficient for x. Since $ 8x > 7x $, subtract $ 7x $ from both sides to get $ x $ on the left.

Q: What if I get a negative answer?

Negative answers are completely normal! Many linear equations have negative solutions. Just make sure to check your work by substituting back into the original equation.

Q: Can I move the 8x to the right side instead?

Absolutely! Subtract $ 8x $ from both sides: $ -1 = 7x - 8x + 5 $, which gives $ -1 = -x + 5 $. Then $ -6 = -x $, so $ x = 6 $.

Q: How do I remember which operation undoes which?

Use opposite operations! Addition undoes subtraction, and subtraction undoes addition. If you see $ +7x $, subtract $ 7x $ to cancel it out.

Linear Equations with Variable Terms

Solve for X:

$8x - 1 = 7x + 5$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$8x - 1 = 7x + 5$

Step-by-step solution

Start by moving the $7x$ term to the left side by subtracting $7x$ from both sides:
$8x - 7x - 1 = 7x + 5 - 7x$
This simplifies to:
$x - 1 = 5$

Next, add $1$ to both sides to isolate $x$ :
$x - 1 + 1 = 5 + 1$
Simplifying this, we get:
$x = 6$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Variable Isolation: Move all x terms to one side first
Technique: Subtract $7x$ from both sides: $8x - 7x = x$
Check: Substitute $x = 6$ : $8(6) - 1 = 47 \neq 47$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting constants before isolating variable terms
Don't move the -1 and +5 first = creates unnecessary complications! This makes the algebra messier and leads to calculation errors. Always collect like variable terms on one side before handling constants.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Which side should I move the x terms to?

Move terms to whichever side gives you a positive coefficient for x. Since $8x > 7x$ , subtract $7x$ from both sides to get $x$ on the left.

Why did the explanation get x = 6 when the answer is x = 6?

There's an error in the provided explanation! Let me fix it: $8x - 7x - 1 = 5$ gives $x - 1 = 5$ , so $x = 6$ . But checking: $8(6) - 1 = 47$ and $7(6) + 5 = 47$ ✓

What if I get a negative answer?

Negative answers are completely normal! Many linear equations have negative solutions. Just make sure to check your work by substituting back into the original equation.

Can I move the 8x to the right side instead?

Absolutely! Subtract $8x$ from both sides: $-1 = 7x - 8x + 5$ , which gives $-1 = -x + 5$ . Then $-6 = -x$ , so $x = 6$ .

How do I remember which operation undoes which?

Use opposite operations! Addition undoes subtraction, and subtraction undoes addition. If you see $+7x$ , subtract $7x$ to cancel it out.

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