Solve for X in the Linear Equation: x+3=-5+2x

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

Moving all x terms to one side lets you combine them into a single coefficient. This makes it much easier to isolate x and find your answer!

Q: How do I know which terms to move first?

It doesn't matter which you move first! The key is to group like terms - all x terms on one side, all numbers on the other. Choose the approach that gives you positive coefficients when possible.

Q: What if I make a sign error?

Sign errors are very common! Always double-check when moving terms across the equal sign. Remember: what you add to one side, add to both sides; what you subtract from one side, subtract from both sides.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Isolate the unknown X

00:18 Simplify what we can

00:53 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve for X:

$x+3=-5+2x$

2

Step-by-step solution

To solve the equation $x + 3 = -5 + 2x$ , we will proceed with these steps:

Step 1: Simplify and rearrange the terms.
Step 2: Isolate the variable $x$ .
Step 3: Solve for $x$ .

Let's go through each of these steps.

Step 1: Simplify the equation by moving all terms involving $x$ to one side and constant terms to the other. Subtract $x$ from both sides:
$x + 3 - x = -5 + 2x - x$
This simplifies to:
$3 = -5 + x$

Step 2: Add 5 to both sides to isolate $x$ :
$3 + 5 = x$

Step 3: Simplify the result:
$8 = x$

Therefore, the solution to the equation is $x = 8$ .

3

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: Move all x terms to one side and constants to the other
Technique: Subtract x from both sides: 3 = -5 + x
Check: Substitute x = 8: 8 + 3 = -5 + 2(8) → 11 = 11 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting incorrectly when moving terms
Don't just move terms without changing signs = wrong equation! Moving x + 3 to the right side as + x + 3 instead of - x - 3 breaks the balance. Always change the sign when moving terms across the equal sign.

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 the x terms to one side?

+

Moving all x terms to one side lets you combine them into a single coefficient. This makes it much easier to isolate x and find your answer!

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 x terms to the right side instead?

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Absolutely! You can move terms to either side. Some students find it easier to keep positive coefficients, so choose whichever way feels more comfortable.

How do I know which terms to move first?

+

It doesn't matter which you move first! The key is to group like terms - all x terms on one side, all numbers on the other. Choose the approach that gives you positive coefficients when possible.

What if I make a sign error?

+

Sign errors are very common! Always double-check when moving terms across the equal sign. Remember: what you add to one side, add to both sides; what you subtract from one side, subtract from both sides.

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