Solve for X in 4x+4=5x+2: Step-by-Step Linear Equation

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

We want to eliminate the 4x on the left side. Since it's positive (+4x), we subtract 4x from both sides. This follows the rule: do the opposite operation to remove a term.

Q: Can I subtract 5x from both sides instead?

Yes, absolutely! You'd get $ -x + 4 = 2 $, then subtract 4 to get $ -x = -2 $, so $ x = 2 $. Same answer, different path!

Q: What if I get a negative answer?

Negative solutions are completely normal! Always check your work by substituting back into the original equation. If both sides match, your negative answer is correct.

Q: How do I remember which terms to move?

Think of it as collecting like terms: put all x-terms on one side and all numbers on the other side. It doesn't matter which side you choose for variables!

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

Solve for X:

$4x+4=5x+2$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$4x+4=5x+2$

Step-by-step solution

We start with the equation:
$4x + 4 = 5x + 2$

Our goal is to solve for $x$ . To do this, we aim to collect all terms containing $x$ on one side of the equation and constant terms on the other side. First, subtract $4x$ from both sides of the equation to eliminate the $x$ term on the left side:

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

This simplifies the equation to:

$4 = x + 2$

Next, subtract $2$ from both sides to isolate the variable $x$ on the right side:

$4 - 2 = x + 2 - 2$

This gives us:

$2 = x$

Thus, the solution to the equation is $x = 2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Collect all variable terms on one side of equation
Technique: Subtract 4x from both sides: 4 = 5x - 4x + 2
Check: Substitute x = 2: 4(2) + 4 = 12 and 5(2) + 2 = 12 ✓

Common Mistakes

Avoid these frequent errors

Moving terms incorrectly without changing signs
Don't just move 4x to the right side as +4x = wrong answer! This ignores the subtraction rule and breaks the equation balance. Always subtract the same term from both sides to move variables properly.

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 eliminate the 4x on the left side. Since it's positive (+4x), we subtract 4x from both sides. This follows the rule: do the opposite operation to remove a term.

Can I subtract 5x from both sides instead?

Yes, absolutely! You'd get $-x + 4 = 2$ , then subtract 4 to get $-x = -2$ , so $x = 2$ . Same answer, different path!

What if I get a negative answer?

Negative solutions are completely normal! Always check your work by substituting back into the original equation. If both sides match, your negative answer is correct.

How do I remember which terms to move?

Think of it as collecting like terms: put all x-terms on one side and all numbers on the other side. It doesn't matter which side you choose for variables!

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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