Solve the Linear Equation: 11 = a - 16

Q: Why do I need to add 16 to both sides?

Think of an equation like a balanced scale. To keep it balanced, whatever you do to one side, you must do to the other side. Adding 16 to both sides cancels out the -16 on the right.

Q: What if I subtract 11 from both sides instead?

You could try that approach! You'd get $ 0 = a - 27 $, then add 27 to get $ a = 27 $. Same answer, but adding 16 is more direct since we want to isolate a.

Q: How do I know which operation to use?

Look at what's happening to your variable. Since a is being decreased by 16, you need to add 16 to undo that operation and isolate the variable.

Q: What if my answer doesn't look right?

Always check your work by substituting your answer back into the original equation. If $ 11 = 27 - 16 $ gives you $ 11 = 11 $, then you're correct!

Linear Equations with Addition Property

$11=a-16$

$a=\text{?}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's isolate the unknown A, and calculate

00:06 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

$11=a-16$

$a=\text{?}$

Step-by-step solution

To find the value of $a$ , we must solve the given linear equation:

$11 = a - 16$

We aim to isolate $a$ by performing operations that maintain the balance of the equation. Currently, $a$ is being decreased by 16. To reverse this, we need to add 16 to both sides.

Step-by-step:

Start with the given equation: $11 = a - 16$ .
Add 16 to both sides to start isolating $a$ :

$11 + 16 = a - 16 + 16$

This simplifies to:

$27 = a$

Thus, the value of $a$ is 27.

Therefore, the solution to the equation $11 = a - 16$ is $a = 27$ .

Final Answer

$27$

Key Points to Remember

Essential concepts to master this topic

Addition Property: Add the same number to both sides to maintain equality
Technique: Add 16 to both sides: 11 + 16 = a - 16 + 16
Check: Substitute back: 11 = 27 - 16 = 11 ✓

Common Mistakes

Avoid these frequent errors

Adding 16 to only one side of the equation
Don't add 16 to just one side like 11 = a - 16 + 16 = wrong answer! This breaks the balance and creates a false equation. Always add the same number to both sides to keep the equation balanced.

Practice Quiz

Test your knowledge with interactive questions

$$ x+7=14 $$

$x=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to add 16 to both sides?

Think of an equation like a balanced scale. To keep it balanced, whatever you do to one side, you must do to the other side. Adding 16 to both sides cancels out the -16 on the right.

What if I subtract 11 from both sides instead?

You could try that approach! You'd get $0 = a - 27$ , then add 27 to get $a = 27$ . Same answer, but adding 16 is more direct since we want to isolate a.

How do I know which operation to use?

Look at what's happening to your variable. Since a is being decreased by 16, you need to add 16 to undo that operation and isolate the variable.

Can I move -16 to the other side instead?

Yes! Moving -16 to the left side means it becomes +16, giving you $11 + 16 = a$ . This is the same as adding 16 to both sides - just a different way of thinking about it.

What if my answer doesn't look right?

Always check your work by substituting your answer back into the original equation. If $11 = 27 - 16$ gives you $11 = 11$ , then you're correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear Equations (One Variable) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime