Solve for X in 24-8x=-2x: Linear Equation Solution

Q: Why do I need to move the -2x term over first?

You need to collect all variable terms on one side to see the true coefficient of x. When variables are on both sides, you can't solve directly!

Q: Can I move the 8x term instead of the -2x?

Absolutely! You could subtract 8x from both sides to get $ 24 - 8x - 8x = -2x - 8x $, giving you $ 24 - 16x = -10x $. Either way works!

Q: What if I get a negative coefficient for x?

No problem! If you end up with something like $ -6x = -24 $, just divide both sides by the negative number. You'll still get $ x = 4 $.

Q: How do I know which side to move the variable terms to?

It doesn't matter! Choose the side that will give you a positive coefficient for easier calculation. Both methods give the same answer.

Q: Why do we combine like terms after moving?

Combining like terms simplifies the equation to its clearest form. $ 8x - 2x = 6x $ is much easier to work with than keeping terms separate!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 Let's arrange the equation so that one side has only the unknown X

00:24 Let's simplify what we can

00:31 Let's isolate the unknown X and calculate

00:43 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Solve for X:

$24-8x=-2x$

2

Step-by-step solution

To solve the equation $24 - 8x = -2x$ , we need to isolate $x$ . Follow these steps:

Step 1: Move all terms involving $x$ to one side of the equation. Add $8x$ to both sides to get:
$24 = 8x - 2x$
Step 2: Simplify the equation by combining like terms on the right:
$24 = 6x$
Step 3: Solve for $x$ by dividing both sides by 6:
$x = \frac{24}{6}$
Step 4: Simplify the result:
$x = 4$

Therefore, the solution to the problem is $\mathbf{x = 4}$ .

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic

Rule: Move all x terms to one side before combining
Technique: Add 8x to both sides: 24 = 6x
Check: Substitute x = 4: 24 - 8(4) = -2(4) gives -8 = -8 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to move all variable terms to same side
Don't leave x terms on both sides like 24 = 8x - 2x without combining = makes division impossible! This creates confusion about which coefficient to use. Always collect all variable terms on one side first, then combine like terms.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I need to move the -2x term over first?

+

You need to collect all variable terms on one side to see the true coefficient of x. When variables are on both sides, you can't solve directly!

Can I move the 8x term instead of the -2x?

+

Absolutely! You could subtract 8x from both sides to get $24 - 8x - 8x = -2x - 8x$ , giving you $24 - 16x = -10x$ . Either way works!

What if I get a negative coefficient for x?

+

No problem! If you end up with something like $-6x = -24$ , just divide both sides by the negative number. You'll still get $x = 4$ .

How do I know which side to move the variable terms to?

+

It doesn't matter! Choose the side that will give you a positive coefficient for easier calculation. Both methods give the same answer.

Why do we combine like terms after moving?

+

Combining like terms simplifies the equation to its clearest form. $8x - 2x = 6x$ is much easier to work with than keeping terms separate!

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Solve for X in 24-8x=-2x: Linear Equation Solution

Linear Equations with Variable Term Movement

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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 move the -2x term over first?

Can I move the 8x term instead of the -2x?

What if I get a negative coefficient for x?

How do I know which side to move the variable terms to?

Why do we combine like terms after moving?

🌟 Unlock Your Math Potential

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