Solve for X: Finding the Number That Equals -17 When -5 Is Added

Q: Why do I write x + (-5) instead of x - 5?

Both are mathematically equivalent, but writing x + (-5) helps you see exactly what the problem is asking. It clearly shows we're adding a negative number, which matches the problem statement.

Q: How do I add a positive number to both sides when there's already a negative?

When you have x + (-5), adding +5 to both sides creates x + (-5) + 5. The (-5) and +5 cancel out because they're opposites, leaving just x on the left side.

Q: Why is the answer negative if I'm adding positive 5?

You're adding 5 to -17, not to a positive number. When you calculate -17 + 5, you're moving 5 steps toward zero on the number line, giving you -12.

Q: How can I check if -12 is really correct?

Substitute -12 for x in the original problem: -12 + (-5). This equals -17, which matches what the problem asked for!

Linear Equations with Negative Integers

What number results in -17 when -5 is added 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 Find the result on the axis

00:07 The number is directed, negative

00:11 Movement to the negative side on the axis is leftward

00:15 Find which number when we move 5 steps left from it gives the result

00:18 To check, let's take 5 jumps to the right

00:23 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

What number results in -17 when -5 is added to it?

Step-by-step solution

To solve this problem, we need to follow these steps:

Step 1: Write down the equation representing the problem: $x + (-5) = -17$ .
Step 2: Isolate the variable $x$ by performing basic arithmetic operations.

Now, let's work through each step:

Step 1: The equation given by the problem is $x + (-5) = -17$ . This means we need to find a number $x$ that, when -5 is added, results in -17.

Step 2: To solve for $x$ , we need to isolate it. We can do this by adding 5 to both sides of the equation:

$x + (-5) + 5 = -17 + 5$

On the left side, adding 5 cancels out the -5, leaving us with:

$x = -17 + 5$

Now, perform the arithmetic operation on the right-hand side:

$-17 + 5 = -12$

Therefore, the number we are looking for is $x = -12$ .

Thus, the solution to the problem is $-12$ .

Final Answer

$-12$

Key Points to Remember

Essential concepts to master this topic

Equation Setup: Write x + (-5) = -17 to represent the problem
Technique: Add 5 to both sides: x + (-5) + 5 = -17 + 5
Check: Substitute -12 back: -12 + (-5) = -17 ✓

Common Mistakes

Avoid these frequent errors

Confusing addition and subtraction with negative numbers
Don't think 'adding -5' means subtraction = wrong equation setup! This leads to solving the wrong problem entirely. Always write exactly what the problem states: x + (-5) = -17.

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 write x + (-5) instead of x - 5?

Both are mathematically equivalent, but writing x + (-5) helps you see exactly what the problem is asking. It clearly shows we're adding a negative number, which matches the problem statement.

How do I add a positive number to both sides when there's already a negative?

When you have x + (-5), adding +5 to both sides creates x + (-5) + 5. The (-5) and +5 cancel out because they're opposites, leaving just x on the left side.

Why is the answer negative if I'm adding positive 5?

You're adding 5 to -17, not to a positive number. When you calculate -17 + 5, you're moving 5 steps toward zero on the number line, giving you -12.

How can I check if -12 is really correct?

Substitute -12 for x in the original problem: -12 + (-5). This equals -17, which matches what the problem asked for!

What if I accidentally subtract 5 instead of add 5?

If you subtract 5 from both sides, you get x + (-5) - 5 = -17 - 5, which gives x - 10 = -22, so x = -12. You still get the right answer! But it's cleaner to add the opposite.

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