Solve the Linear Equation: -16 + a = -17

Q: Why do I add 16 instead of subtracting 16?

Because we have -16 in the equation, and we want to eliminate it. The opposite of -16 is +16, so adding 16 cancels out the -16 completely!

Q: What if I subtract 16 from both sides instead?

That would give you $ -16 + a - 16 = -17 - 16 $, which simplifies to $ a - 32 = -33 $. Now you have an even more complicated equation to solve!

Q: How do I remember which operation to use?

Think "What cancels out?" If you see +5, subtract 5. If you see -3, add 3. Always use the opposite operation to eliminate terms.

Q: Can I move -16 to the other side instead?

Yes! Moving -16 to the right side gives $ a = -17 - (-16) = -17 + 16 = -1 $. This is the same as adding 16 to both sides.

Q: Why is my answer negative?

Because -17 is less than -16! When you add a small positive number (1) to -16, you get -15, not -17. You need to add a negative number (-1) to get -17.

Linear Equations with Negative Constants

$-16+a=-17$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the value of A.

00:07 Arrange the equation so only the unknown A is on one side.

00:12 Now, let's group similar terms together.

00:15 And that's how we solve for A!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-16+a=-17$

Step-by-step solution

Let's solve the equation $-16 + a = -17$ by isolating the variable $a$ .

To isolate $a$ , add 16 to both sides of the equation to cancel out the $-16$ :

$-16 + a + 16 = -17 + 16$

This simplification results in:

$a = -1$

Thus, the solution to the equation $-16 + a = -17$ is $a = -1$ .

If we review the answer choices given, the correct answer is Choice 4, $-1$ .

The solution to the problem is $a = -1$ .

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Rule: Use inverse operations to isolate the variable completely
Technique: Add 16 to both sides: $-16 + a + 16 = -17 + 16$
Check: Substitute back: $-16 + (-1) = -17$ ✓

Common Mistakes

Avoid these frequent errors

Adding the wrong number to both sides
Don't add the same number that's already in the equation = no change! Adding -16 to both sides gives -16 + a - 16 = -17 - 16, which makes a = -33. Always add the opposite (inverse) of the number you want to eliminate.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I add 16 instead of subtracting 16?

Because we have -16 in the equation, and we want to eliminate it. The opposite of -16 is +16, so adding 16 cancels out the -16 completely!

What if I subtract 16 from both sides instead?

That would give you $-16 + a - 16 = -17 - 16$ , which simplifies to $a - 32 = -33$ . Now you have an even more complicated equation to solve!

How do I remember which operation to use?

Think "What cancels out?" If you see +5, subtract 5. If you see -3, add 3. Always use the opposite operation to eliminate terms.

Can I move -16 to the other side instead?

Yes! Moving -16 to the right side gives $a = -17 - (-16) = -17 + 16 = -1$ . This is the same as adding 16 to both sides.

Why is my answer negative?

Because -17 is less than -16! When you add a small positive number (1) to -16, you get -15, not -17. You need to add a negative number (-1) to get -17.

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