Solve the Linear Equation: 2a + 3a + 45a = 0

Q: Why is the answer 0 and not some other number?

When any number is multiplied by zero, the result is always zero. Since $ 50a = 0 $, the only value of a that makes this true is $ a = 0 $.

Q: What does it mean to combine like terms?

Like terms have the same variable with the same power. Here, $ 2a $, $ 3a $, and $ 45a $ are all like terms because they all contain a to the first power.

Q: How do I add the coefficients correctly?

The coefficients are the numbers in front of the variable. Simply add them: $ 2 + 3 + 45 = 50 $, so you get $ 50a $.

Q: Could the answer ever be something other than 0?

No! When you have $ 50a = 0 $, dividing both sides by 50 gives $ a = \frac{0}{50} = 0 $. Zero divided by any non-zero number is always zero.

Linear Equations with Zero Solutions

$2a+3a+45a=0$

$a=\text{?}$

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Step-by-step video solution

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00:00 Found A

00:03 Gathering factors

00:11 Isolate A

00:18 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

$2a+3a+45a=0$

$a=\text{?}$

Step-by-step solution

To solve the equation $2a + 3a + 45a = 0$ , follow these steps:

Step 1: Combine Like Terms.

Add the coefficients of $a$ :

$2 + 3 + 45 = 50$

Step 2: Substitute and Simplify.

This simplifies the equation to:

$50a = 0$

Step 3: Solve for $a$ .

To find $a$ , divide both sides of the equation by 50:

$a = \frac{0}{50}$

$a = 0$

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

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Combining Like Terms: Add coefficients of same variables together
Technique: Calculate 2 + 3 + 45 = 50, so 50a = 0
Check: Substitute a = 0: 2(0) + 3(0) + 45(0) = 0 ✓

Common Mistakes

Avoid these frequent errors

Solving each term separately instead of combining like terms first
Don't try to solve 2a = 0, then 3a = 0, then 45a = 0 separately = confusing multiple solutions! This creates unnecessary work and can lead to errors. Always combine like terms first to get one simplified equation.

Practice Quiz

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$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why is the answer 0 and not some other number?

When any number is multiplied by zero, the result is always zero. Since $50a = 0$ , the only value of a that makes this true is $a = 0$ .

What does it mean to combine like terms?

Like terms have the same variable with the same power. Here, $2a$ , $3a$ , and $45a$ are all like terms because they all contain a to the first power.

How do I add the coefficients correctly?

The coefficients are the numbers in front of the variable. Simply add them: $2 + 3 + 45 = 50$ , so you get $50a$ .

Could the answer ever be something other than 0?

No! When you have $50a = 0$ , dividing both sides by 50 gives $a = \frac{0}{50} = 0$ . Zero divided by any non-zero number is always zero.

What if I forgot to combine like terms?

You might get confused trying to solve multiple separate equations. Always combine like terms first - it simplifies the problem and prevents errors!

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