Solve the Linear Equation: 3 + x - 2 = 7 - 3 Step-by-Step

Q: Why do I need to simplify both sides first?

Simplifying first makes the equation much easier to solve! Instead of working with $ 3 + x - 2 = 7 - 3 $, you get the cleaner equation $ 1 + x = 4 $.

Q: Can I move terms across the equals sign right away?

You could, but it's much more confusing! It's better to combine like terms on each side first, then use inverse operations to isolate x.

Q: What if I get the same number on both sides after simplifying?

If you get something like $ 5 = 5 $ after simplifying, that means every number works for x! The equation has infinitely many solutions.

Q: How do I know which terms to combine?

Combine constant numbers together (like 3 and -2) and variable terms together (like 2x and 5x). Keep them on their original sides of the equation.

Q: What's the difference between 3 + x - 2 and 3 - 2 + x?

They're exactly the same! Addition is commutative, so you can rearrange terms. Both equal $ 1 + x $ or $ x + 1 $.

Linear Equations with Constant Simplification

Solve for X:

$3 + x - 2 = 7 - 3$

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Step-by-step video solution

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Step-by-step written solution

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Understand the problem

Solve for X:

$3 + x - 2 = 7 - 3$

Step-by-step solution

First, simplify both sides of the equation:

Left side: $3 + x - 2 = 1 + x$

Right side: $7 - 3 = 4$

So the equation becomes:

$1 + x = 4$

Next, isolate $x$ by subtracting 1 from both sides:

$1 + x - 1 = 4 - 1$

This simplifies to:

$x = 3$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Simplification Rule: Combine like terms on each side before isolating variables
Technique: Calculate $3 - 2 = 1$ and $7 - 3 = 4$ first
Check: Substitute x = 3: $3 + 3 - 2 = 4$ and $7 - 3 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Trying to isolate x without simplifying constants first
Don't jump straight to moving terms across the equals sign = messy calculations with multiple steps! This leads to arithmetic errors and confusion. Always simplify both sides completely before isolating the variable.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to simplify both sides first?

Simplifying first makes the equation much easier to solve! Instead of working with $3 + x - 2 = 7 - 3$ , you get the cleaner equation $1 + x = 4$ .

Can I move terms across the equals sign right away?

You could, but it's much more confusing! It's better to combine like terms on each side first, then use inverse operations to isolate x.

What if I get the same number on both sides after simplifying?

If you get something like $5 = 5$ after simplifying, that means every number works for x! The equation has infinitely many solutions.

How do I know which terms to combine?

Combine constant numbers together (like 3 and -2) and variable terms together (like 2x and 5x). Keep them on their original sides of the equation.

What's the difference between 3 + x - 2 and 3 - 2 + x?

They're exactly the same! Addition is commutative, so you can rearrange terms. Both equal $1 + x$ or $x + 1$ .

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Solve the Linear Equation: 3 + x - 2 = 7 - 3 Step-by-Step

Linear Equations with Constant Simplification

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to simplify both sides first?

Can I move terms across the equals sign right away?

What if I get the same number on both sides after simplifying?

How do I know which terms to combine?

What's the difference between 3 + x - 2 and 3 - 2 + x?

🌟 Unlock Your Math Potential

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