Solve the Equation: Finding the Missing Number in 5 + (?) = -6

Q: Why is the answer negative when we're adding?

Great question! Even though we're adding something to 5, that 'something' can be negative. Adding a negative number is the same as subtracting: $ 5 + (-11) = 5 - 11 = -6 $

Q: What if I got +11 as my answer?

That's a common mistake! If you add $ 5 + 11 = 16 $, which is nowhere near -6. Remember: moving left on the number line means subtracting or adding a negative number.

Q: Can I use subtraction instead of addition?

Yes! You can rewrite this as $ 5 - ? = -6 $. Then solve: $ ? = 5 - (-6) = 5 + 6 = 11 $. So we subtract 11, which is the same as adding -11.

Q: How do I check my work?

Substitute your answer back into the original equation: $ 5 + (-11) = -6 $. If both sides are equal, you're correct! Always use the original equation to verify.

Linear Equations with Negative Solutions

$5+(?)=-6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 First, let's complete the missing number.

00:07 The number moves to the right and it's positive.

00:12 Since the right is positive, we'll move 5 steps to the right.

00:18 Now, let's find this number on the number line.

00:24 We need to measure its distance from point 5.

00:33 Remember, moving left means going in the negative direction.

00:49 Great job! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5+(?)=-6$

Step-by-step solution

To know how much we need to add to the number 5 to get minus 6, we will count the number of steps between the numbers.

Also, we'll pay attention to which direction we moved, if we went right then the number is positive, if we went left the number will be negative.

We'll locate the number 5, and move left until we reach minus 6, where each step represents one whole number, as follows:

We'll discover that the number of steps is 11, since we went left, the number will be minus 11.

Final Answer

$-11$

Key Points to Remember

Essential concepts to master this topic

Rule: To isolate the unknown, subtract 5 from both sides
Technique: Move from 5 to -6 requires going 11 steps left
Check: Verify: 5 + (-11) = -6 equals our target ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting to solve
Don't think 'what plus 5 equals -6' means add something positive = wrong sign! This ignores that we need to move left on the number line. Always subtract 5 from both sides: ? = -6 - 5 = -11.

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 the answer negative when we're adding?

Great question! Even though we're adding something to 5, that 'something' can be negative. Adding a negative number is the same as subtracting: $5 + (-11) = 5 - 11 = -6$

How do I count steps on the number line?

Start at your first number (5) and count each unit until you reach your target (-6). Since you're moving left (toward negative numbers), your answer will be negative. Count: 11 steps left means -11.

What if I got +11 as my answer?

That's a common mistake! If you add $5 + 11 = 16$ , which is nowhere near -6. Remember: moving left on the number line means subtracting or adding a negative number.

Can I use subtraction instead of addition?

Yes! You can rewrite this as $5 - ? = -6$ . Then solve: $? = 5 - (-6) = 5 + 6 = 11$ . So we subtract 11, which is the same as adding -11.

How do I check my work?

Substitute your answer back into the original equation: $5 + (-11) = -6$ . If both sides are equal, you're correct! Always use the original equation to verify.

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