Solve the Linear Equation: Applying Distributive Property in 3(a+1) - 3 = 0

Q: What does it mean to distribute in math?

Distribution means multiplying the number outside parentheses by every term inside. Think of it as sharing equally: $ 3(a+1) $ becomes $ 3 \times a + 3 \times 1 $.

Q: Why do the +3 and -3 cancel out?

Because $ +3 - 3 = 0 $! These are like terms (both constants) that combine to zero, leaving us with just $ 3a = 0 $.

Q: How do I know when to use the distributive property?

Look for a number or variable outside parentheses. Whenever you see something like $ 3(a+1) $ or $ -2(x-4) $, you need to distribute first!

Q: What if I get zero as my answer?

Zero is a perfectly valid answer! Many equations have $ x = 0 $ or $ a = 0 $ as solutions. Always check by substituting back into the original equation.

Q: Can I solve this without distributing?

You could try other methods, but distributing first is usually the clearest approach. It follows the standard order of operations and helps avoid mistakes.

Linear Equations with Distributive Property

$3(a+1)-3=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem together.

00:09 First, open the brackets carefully, and multiply each term by the factors inside.

00:17 Next, collect like terms to simplify the expression.

00:29 Then, isolate the variable A on one side of the equation.

00:36 And that's how you find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3(a+1)-3=0$

Step-by-step solution

Let's proceed to solve the linear equation $3(a+1) - 3 = 0$ :

Step 1: Distribute the 3 in the expression $3(a+1)$ .

We get:
$3 \cdot a + 3 \cdot 1 - 3 = 0$

This simplifies to:
$3a + 3 - 3 = 0$

Step 2: Simplify the expression by combining like terms.

We simplify this to:
$3a + 0 = 0$ or simply $3a = 0$

Step 3: Isolate $a$ by dividing both sides by 3.

$\frac{3a}{3} = \frac{0}{3}$

Thus,
$a = 0$

Therefore, the solution to the problem is $a = 0$ .

The correct choice is the option corresponding to $a = 0$ .

Final Answer

$a=0$

Key Points to Remember

Essential concepts to master this topic

Distributive Rule: Multiply outside term by each term inside parentheses
Technique: $3(a+1) = 3a + 3$ then combine like terms
Check: Substitute $a = 0$ : $3(0+1) - 3 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Not distributing to all terms inside parentheses
Don't just multiply 3 × a and forget the +1 = $3a - 3 = 0$ giving wrong answer! This skips a term and creates an entirely different equation. Always distribute the outside number to every single term inside the parentheses.

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

What does it mean to distribute in math?

Distribution means multiplying the number outside parentheses by every term inside. Think of it as sharing equally: $3(a+1)$ becomes $3 \times a + 3 \times 1$ .

Why do the +3 and -3 cancel out?

Because $+3 - 3 = 0$ ! These are like terms (both constants) that combine to zero, leaving us with just $3a = 0$ .

How do I know when to use the distributive property?

Look for a number or variable outside parentheses. Whenever you see something like $3(a+1)$ or $-2(x-4)$ , you need to distribute first!

What if I get zero as my answer?

Zero is a perfectly valid answer! Many equations have $x = 0$ or $a = 0$ as solutions. Always check by substituting back into the original equation.

Can I solve this without distributing?

You could try other methods, but distributing first is usually the clearest approach. It follows the standard order of operations and helps avoid mistakes.

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