Solve the Linear Equation: 2x + 4 = 3x - 5 Step by Step

Q: Why do I need to move all x terms to one side?

Moving all variable terms to one side makes it easier to solve! You end up with something like $ x = 9 $ instead of having x scattered on both sides.

Q: How do I know when I'm done solving?

You're done when you have x by itself on one side of the equation, like $ x = 9 $. Always verify by substituting this value back into the original equation!

Linear Equations with Variable Terms

Solve for X:

$2x + 4 = 3x - 5$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$2x + 4 = 3x - 5$

Step-by-step solution

To solve for $x$ , first, we need to get all terms involving $x$ on one side of the equation and constant terms on the other. Start with the original equation:

$2x + 4 = 3x - 5$

Subtract $2x$ from both sides to isolate the term involving $x$ on one side:

$4 = x - 5$

Next, add 5 to both sides to isolate $x$ :

$9 = x$

Thus, the value of $x$ is $9$ .

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Balance Rule: What you do to one side, do to the other
Technique: Move all x terms to one side: 3x - 2x = x
Check: Substitute x = 9: 2(9) + 4 = 22, 3(9) - 5 = 22 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting from only one side
Don't subtract 2x from just the left side = 4 = 3x - 5! This breaks the equation balance and gives x = 3 instead of 9. Always perform the same operation on both sides to maintain equality.

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 move all x terms to one side?

Moving all variable terms to one side makes it easier to solve! You end up with something like $x = 9$ instead of having x scattered on both sides.

Which side should I move the x terms to?

It doesn't matter! You can move them to either side. Choose whichever gives you a positive coefficient for x to avoid working with negative numbers.

What if I get a negative answer?

Negative solutions are completely normal! Just make sure to check your work by substituting back into the original equation to verify it's correct.

Can I solve this equation differently?

Yes! You could start by adding 5 to both sides, then subtracting 4. The key is to use inverse operations and maintain balance throughout.

How do I know when I'm done solving?

You're done when you have x by itself on one side of the equation, like $x = 9$ . Always verify by substituting this value back into the original equation!

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