Solve the Equation: Finding m in 2(m+8)-3(16+m)=0

Q: Why do I need to distribute before combining like terms?

You must distribute first to remove parentheses and see all terms clearly. If you try to combine terms while they're still in parentheses, you'll make mistakes with signs and coefficients.

Q: How do I handle the negative sign in front of 3(16+m)?

The negative sign belongs to the 3, so you have $ -3(16 + m) $. This means you distribute negative 3 to both terms: $ -3 \times 16 = -48 $ and $ -3 \times m = -3m $.

Q: What if I get confused combining like terms?

Group similar terms together: put all m terms together and all number terms together. For example: $ 2m - 3m $ and $ 16 - 48 $ separately.

Q: How can I check if m = -32 is correct?

Substitute back into the original equation: $ 2(-32 + 8) - 3(16 + (-32)) = 2(-24) - 3(-16) = -48 + 48 = 0 $ ✓

Linear Equations with Distribution and Combining Terms

$2(m+8)-3(16+m)=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Open parentheses properly, multiply by each factor

00:23 Collect terms

00:35 Arrange the equation so that only the unknown M is on one side

00:43 Convert from negative to positive

00:52 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2(m+8)-3(16+m)=0$

Step-by-step solution

To solve the given equation $2(m+8) - 3(16+m) = 0$ , we will follow these steps:

Step 1: Apply the distributive property to expand the expression.
Step 2: Combine like terms on both sides of the equation.
Step 3: Solve for $m$ by isolating it.

Let's go through each step:

Step 1: Apply the distributive property:
Expand $2(m+8)$ to get $2m + 16$ .
Expand $-3(16+m)$ to get $-48 - 3m$ .

Step 2: Combine these expressions:
The equation becomes $2m + 16 - 48 - 3m = 0$ .

Simplify it:
Combine like terms: $(2m - 3m) + (16 - 48)$ .
This simplifies to $-m - 32 = 0$ .

Step 3: Solve for $m$ :
To isolate $m$ , add 32 to both sides:
$-m = 32$ .

Multiply both sides by -1 to solve for $m$ :
$m = -32$ .

Thus, the solution to the equation is $\mathbf{m = -32}$ .

Final Answer

$m=-32$

Key Points to Remember

Essential concepts to master this topic

Distribution: Apply distributive property to expand all parentheses first
Technique: Combine like terms: $2m - 3m = -m$ and $16 - 48 = -32$
Check: Substitute $m = -32$ : $2(-24) - 3(-16) = -48 + 48 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly distributing negative signs
Don't distribute -3 to get $-48 + 3m$ = wrong sign on variable term! This happens when you forget the negative distributes to ALL terms. Always remember: $-3(16 + m) = -48 - 3m$ .

Practice Quiz

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$$ 5x=1 $$

What is the value of x?

FAQ

Everything you need to know about this question

Why do I need to distribute before combining like terms?

You must distribute first to remove parentheses and see all terms clearly. If you try to combine terms while they're still in parentheses, you'll make mistakes with signs and coefficients.

How do I handle the negative sign in front of 3(16+m)?

The negative sign belongs to the 3, so you have $-3(16 + m)$ . This means you distribute negative 3 to both terms: $-3 \times 16 = -48$ and $-3 \times m = -3m$ .

What if I get confused combining like terms?

Group similar terms together: put all m terms together and all number terms together. For example: $2m - 3m$ and $16 - 48$ separately.

Why is the final answer negative?

Don't worry about negative answers! They're completely valid solutions. The key is following the algebra correctly. When you get $-m = 32$ , multiply both sides by -1 to get $m = -32$ .

How can I check if m = -32 is correct?

Substitute back into the original equation: $2(-32 + 8) - 3(16 + (-32)) = 2(-24) - 3(-16) = -48 + 48 = 0$ ✓

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