Solve for X: Finding the Solution to 9x-3=10x+1

Q: Why do I subtract 9x instead of 10x from both sides?

You can subtract either one! Subtracting 9x gives you $ -3 = x + 1 $, while subtracting 10x gives you $ -x - 3 = 1 $. Both work, but subtracting the smaller coefficient usually keeps the math simpler.

Q: How do I avoid sign errors when moving terms?

Remember: when you move a term across the equal sign, it changes sign. So $ 9x - 3 $ becomes $ -3 $ when you subtract $ 9x $ from both sides.

Q: What's the fastest way to solve this type of equation?

Look at the coefficients of x first. Since you have 9x and 10x, subtract the smaller one (9x) from both sides. This immediately gives you a simpler equation with x on just one side!

Linear Equations with Variable Distribution

Solve for X:

$9x-3=10x+1$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$9x-3=10x+1$

Step-by-step solution

To solve the equation $9x - 3 = 10x + 1$ , we need to get all terms with $x$ on one side and constant terms on the other side. Here's how we do it step-by-step:

First, subtract $9x$ from both sides of the equation to start getting $x$ terms on one side. This gives us: $-3 = x + 1$
Next, subtract 1 from both sides to isolate $x$ . We get: $-3 - 1 = x$
Simplifying the left side, we find: $x = -4$

Therefore, the solution is $x = -4$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Distribution: Move all x terms to one side, constants to other
Technique: Subtract 9x from both sides: -3 = x + 1
Check: Substitute x = -4: 9(-4) - 3 = 10(-4) + 1 gives -39 = -39 ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting when moving terms
Don't add 9x to both sides when you see 9x - 3 = 10x + 1 = gets 18x - 3 = 1! This moves terms in the wrong direction and creates a harder equation. Always subtract the smaller coefficient from both sides to isolate variables properly.

Practice Quiz

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$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do I subtract 9x instead of 10x from both sides?

You can subtract either one! Subtracting 9x gives you $-3 = x + 1$ , while subtracting 10x gives you $-x - 3 = 1$ . Both work, but subtracting the smaller coefficient usually keeps the math simpler.

What if I get a negative answer like x = -4?

Negative answers are completely normal! Many equations have negative solutions. Don't second-guess yourself - just always check by substituting back into the original equation.

Can I move the constants first instead of the variables?

Yes! You could subtract 1 from both sides first, then add 3 to both sides. The order doesn't matter as long as you do the same operation to both sides each time.

How do I avoid sign errors when moving terms?

Remember: when you move a term across the equal sign, it changes sign. So $9x - 3$ becomes $-3$ when you subtract $9x$ from both sides.

What's the fastest way to solve this type of equation?

Look at the coefficients of x first. Since you have 9x and 10x, subtract the smaller one (9x) from both sides. This immediately gives you a simpler equation with x on just one side!

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