Solve for X: -9(2-x) = (x+4)×3 Linear Equation Challenge

Q: Why does -9 times -x give +9x?

Remember the rule: negative times negative equals positive! When you distribute -9(2-x), you get -9(2) + (-9)(-x) = -18 + 9x.

Q: How do I keep track of all the signs?

Write each step clearly and double-check your signs. When moving terms across the equals sign, remember to change their signs: +3x becomes -3x, and -18 becomes +18.

Q: What if I get the wrong answer when checking?

Go back and check your distribution step first - that's where most sign errors happen. Then verify each step of combining like terms and solving.

Q: Can I solve this equation differently?

Yes! You could distribute the 3 first: $ -9(2-x) = 3x + 12 $. Both methods work, but always start by distributing to eliminate parentheses.

Q: Why do we move terms to different sides?

We want to isolate the variable by getting all x-terms on one side and all numbers on the other. This makes it easier to solve for x!

Linear Equations with Distributive Property

Solve for x:

$-9(2-x)=(x+4)\cdot3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's begin by finding X. Ready? Here we go!

00:12 First, open the parentheses and multiply each term. Take your time!

00:33 Next, arrange the equation so that only the X is on one side. Great job so far!

00:48 Now, let's collect like terms together. Almost there!

00:53 Finally, isolate X to find the answer. You’re doing amazing!

01:01 And that's how we solve this problem! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for x:

$-9(2-x)=(x+4)\cdot3$

Step-by-step solution

We open the parentheses in both sections by the distributive property and use the formula:

$a(x+b)=ax+ab$

$-18+9x=3x+12$

We move 3X to the left section, and 18 to the right section and maintain the corresponding signs:

$9x-3x=12+18$

We add the terms:

$6x=30$

We divide both sections by 6:

$\frac{6x}{6}=\frac{30}{6}$

$x=5$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply terms inside parentheses by outside coefficient
Technique: Combine like terms: $9x - 3x = 6x$
Check: Substitute x = 5: $-9(-3) = 27$ and $(9)(3) = 27$ ✓

Common Mistakes

Avoid these frequent errors

Incorrect distribution of negative signs
Don't forget the negative sign when distributing: -9(2-x) = -18-9x is wrong! The negative nine times negative x gives positive 9x. Always distribute carefully: -9(2-x) = -18 + 9x.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why does -9 times -x give +9x?

Remember the rule: negative times negative equals positive! When you distribute -9(2-x), you get -9(2) + (-9)(-x) = -18 + 9x.

How do I keep track of all the signs?

Write each step clearly and double-check your signs. When moving terms across the equals sign, remember to change their signs: +3x becomes -3x, and -18 becomes +18.

What if I get the wrong answer when checking?

Go back and check your distribution step first - that's where most sign errors happen. Then verify each step of combining like terms and solving.

Can I solve this equation differently?

Yes! You could distribute the 3 first: $-9(2-x) = 3x + 12$ . Both methods work, but always start by distributing to eliminate parentheses.

Why do we move terms to different sides?

We want to isolate the variable by getting all x-terms on one side and all numbers on the other. This makes it easier to solve for x!

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