Solve for X: Finding the Number That Plus -4 Equals 7

Q: Why is adding -4 the same as subtracting 4?

Adding a negative number has the same effect as subtracting! Think of it on a number line: moving 4 steps left is the same whether you 'add -4' or 'subtract 4'.

Q: How do I know what operation undoes adding -4?

To undo any addition, you do the opposite operation. Since adding -4 moves you 4 steps left, you need to move 4 steps right by adding +4.

Q: Can I rewrite the equation to make it easier?

Absolutely! You can rewrite $ x + (-4) = 7 $ as $ x - 4 = 7 $. Both forms mean the same thing!

Q: Is there a pattern for these types of problems?

If x + a = b, then x = b - aFor our problem: x + (-4) = 7, so x = 7 - (-4) = 7 + 4 = 11

Linear Equations with Negative Number Operations

Which number gives us 7 if we add -4 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 Isolate the unknown

00:20 Reduce what's possible

00:36 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which number gives us 7 if we add -4 to it?

Step-by-step solution

To solve this problem, we begin by formulating it as an algebraic equation based on the information given. We are asked to find a number such that adding -4 to it yields 7. Mathematically, this can be expressed as:

$x + (-4) = 7$

which simplifies to:

$x - 4 = 7$

We solve for $x$ by adding 4 to both sides of the equation to isolate the variable:

$x - 4 + 4 = 7 + 4$

This results in:

$x = 11$

Therefore, the number we are looking for is $11$ .

Final Answer

$11$

Key Points to Remember

Essential concepts to master this topic

Setup: Translate word problem into equation form x + (-4) = 7
Technique: Add opposite of -4, which is +4, to both sides: x = 7 + 4 = 11
Check: Substitute back into original: 11 + (-4) = 11 - 4 = 7 ✓

Common Mistakes

Avoid these frequent errors

Confusing which operation undoes adding negative numbers
Don't subtract 4 from both sides when solving x + (-4) = 7, giving x = 3! Adding a negative is the same as subtracting, so you need to ADD the positive to undo it. Always add +4 to both sides to isolate x.

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 is adding -4 the same as subtracting 4?

Adding a negative number has the same effect as subtracting! Think of it on a number line: moving 4 steps left is the same whether you 'add -4' or 'subtract 4'.

How do I know what operation undoes adding -4?

To undo any addition, you do the opposite operation. Since adding -4 moves you 4 steps left, you need to move 4 steps right by adding +4.

Can I rewrite the equation to make it easier?

Absolutely! You can rewrite $x + (-4) = 7$ as $x - 4 = 7$ . Both forms mean the same thing!

What if I got -7 or 7 as my answer?

Check your work! If you got -7: (-7) + (-4) = -11, not 7. If you got 7: (7) + (-4) = 3, not 7. Only 11 works: (11) + (-4) = 7 ✓

Is there a pattern for these types of problems?

If x + a = b, then x = b - a
For our problem: x + (-4) = 7, so x = 7 - (-4) = 7 + 4 = 11

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