Solve for X: Finding the Number That Gives -24 When Adding -3

Q: Why do I add 3 to both sides if the problem says add -3?

Great question! To isolate x, you need to undo what's being done to it. Since -3 is being added to x, you add the opposite (+3) to both sides to cancel it out.

Q: What if I get confused about which operation to use?

Think of it as undoing what's happening to x. If something is being added, subtract it. If something is being subtracted, add it. Always do the opposite operation!

Q: How can I check if -21 is really correct?

Substitute -21 back into the original situation: $ -21 + (-3) = -24 $. Since this equals -24, your answer is correct!

Solving Linear Equations with Negative Numbers

Which number gives us -24 when we add -3 to it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 The number is intentional, negative

00:07 Movement to the negative side on the axis is leftward

00:13 Find the result on the axis

00:16 Find which number, when moving 3 units left from it, gives the result

00:26 To verify, take 3 jumps to the right

00:36 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

Which number gives us -24 when we add -3 to it?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Set up the equation using the given information.
Step 2: Rearrange the equation to solve for $x$ .
Step 3: Calculate the value of $x$ .

Now, let's work through each step:

Step 1: We are given that adding $-3$ to a number $x$ results in $-24$ . This can be written as:
$x + (-3) = -24$ .

Step 2: To isolate $x$ , we add 3 to both sides of the equation, as $-3$ is the term being added:
$x + (-3) + 3 = -24 + 3$ .

Step 3: Simplifying the equation gives us:
$x = -24 + 3$ .
Perform the addition on the right-hand side:
$x = -21$ .

Therefore, the solution to the problem is that the number is $-21$ .

Final Answer

$-21$

Key Points to Remember

Essential concepts to master this topic

Setup: Write the equation from the word problem description
Technique: Add the opposite: x + (-3) = -24, so add +3 to both sides
Check: Substitute back: -21 + (-3) = -24 ✓

Common Mistakes

Avoid these frequent errors

Adding -3 instead of subtracting it from -24
Don't solve by doing -24 + (-3) = -27! This gives the wrong answer because you're adding the same number twice. Always add the opposite of what's being added to the variable to isolate it.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why do I add 3 to both sides if the problem says add -3?

Great question! To isolate x, you need to undo what's being done to it. Since -3 is being added to x, you add the opposite (+3) to both sides to cancel it out.

How do I handle adding negative numbers?

When adding a negative number like -3, it's the same as subtracting the positive version. So $x + (-3)$ is the same as $x - 3$ .

What if I get confused about which operation to use?

Think of it as undoing what's happening to x. If something is being added, subtract it. If something is being subtracted, add it. Always do the opposite operation!

How can I check if -21 is really correct?

Substitute -21 back into the original situation: $-21 + (-3) = -24$ . Since this equals -24, your answer is correct!

Why is the answer negative?

The answer is negative because we're looking for a number that becomes even more negative when we add -3 to it. Since -21 is already negative, adding another negative makes it -24.

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