Solve the Linear Equation: Finding X in 5x+2=4x+10

Q: Why do I subtract 4x from both sides instead of adding?

We want to isolate the variable terms on one side. Since we have $ 5x $ and $ 4x $, subtracting $ 4x $ from both sides leaves us with just $ x $ on the left!

Q: Can I move the 5x to the right side instead?

Absolutely! You could subtract $ 5x $ from both sides to get $ 2 = -x + 10 $, then solve for $ x $. Both methods give the same answer: $ x = 8 $.

Q: How do I remember which operations to use?

Think of it as undoing what's been done to the variable. If something is added, subtract it. If something is subtracted, add it. Always do the opposite operation to both sides.

Q: Why does my teacher want me to show every step?

Showing steps helps you avoid mistakes and makes it easier to find errors. Plus, partial credit is often given for correct steps even if the final answer is wrong!

Linear Equations with Variable Terms Isolation

Solve for X:

$5x+2=4x+10$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$5x+2=4x+10$

Step-by-step solution

To solve the equation $5x + 2 = 4x + 10$ , we can simplify and solve for $x$ by following these steps:

First, let's get all terms involving $x$ on one side and the constant terms on the other. We do this by subtracting $4x$ from both sides:

$5x + 2 - 4x = 4x + 10 - 4x$

This simplifies to:

$x + 2 = 10$
Next, we need to isolate $x$ by subtracting 2 from both sides:

$x + 2 - 2 = 10 - 2$

Which simplifies to:

$x = 8$

Thus, the solution for $x$ is $8$ .

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: Move variable terms to one side, constants to other
Technique: Subtract $4x$ from both sides: $x + 2 = 10$
Check: Substitute $x = 8$ : $5(8) + 2 = 4(8) + 10 = 42$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting variable terms incorrectly
Don't subtract $4x$ from only one side = unbalanced equation giving wrong answers! This violates the fundamental rule of equations. Always perform the same operation on both sides simultaneously.

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 subtract 4x from both sides instead of adding?

We want to isolate the variable terms on one side. Since we have $5x$ and $4x$ , subtracting $4x$ from both sides leaves us with just $x$ on the left!

Can I move the 5x to the right side instead?

Absolutely! You could subtract $5x$ from both sides to get $2 = -x + 10$ , then solve for $x$ . Both methods give the same answer: $x = 8$ .

What if I get a negative answer?

Negative answers are completely normal in algebra! The key is to check your work by substituting back into the original equation to make sure both sides are equal.

How do I remember which operations to use?

Think of it as undoing what's been done to the variable. If something is added, subtract it. If something is subtracted, add it. Always do the opposite operation to both sides.

Why does my teacher want me to show every step?

Showing steps helps you avoid mistakes and makes it easier to find errors. Plus, partial credit is often given for correct steps even if the final answer is wrong!

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