Solve the Linear Equation: -3 + X = -8 for X

Q: Why do I add 3 when the equation shows -3?

You add 3 because it's the opposite operation that cancels out -3. Think of it as: -3 + 3 = 0, which eliminates the constant from the left side completely.

Q: What if I accidentally subtract 3 from both sides?

You'll get $ x = -11 $, which is wrong! Always check by substituting back: $ -3 + (-11) = -14 \neq -8 $. When you see your check doesn't work, try the opposite operation.

Q: How do I remember which operation to use?

Use the opposite operation to cancel out constants. If you see +5, subtract 5. If you see -3, add 3. The goal is always to make the constant disappear by getting zero.

Q: Can I move -3 to the right side instead?

Yes! Moving -3 to the right side gives: $ x = -8 - (-3) = -8 + 3 = -5 $. This is the same as adding 3 to both sides, just thinking about it differently.

Q: What does 'isolate the variable' actually mean?

Isolating the variable means getting the letter (like x) by itself on one side of the equation. You want: $ x = \text{some number} $, with nothing else attached to x.

Linear Equations with Negative Constants

Solve for X:

$-3+x=-8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Let's arrange the equation so that X (the unknown) is on one side

00:11 Collect like terms

00:17 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

Solve for X:

$-3+x=-8$

Step-by-step solution

To solve the equation $-3 + x = -8$ , we need to isolate the variable $x$ . We can do this by eliminating the constant term on the side with the variable.

Step 1: Add 3 to both sides of the equation to cancel out the $-3$ next to $x$ .
This gives us:

$-3 + x + 3 = -8 + 3$

Step 2: Simplifying both sides of the equation results in:

$x = -5$

Therefore, the solution to the equation is $x = -5$ , which matches choice 2.

Final Answer

-5

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Add or subtract to eliminate constants from variable side
Technique: Add 3 to both sides: $-3 + x + 3 = -8 + 3$
Check: Substitute x = -5: $-3 + (-5) = -8$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting 3 instead of adding 3
Don't subtract 3 from both sides = $x = -11$ ! This makes the negative constant more negative instead of canceling it out. Always do the opposite operation: add 3 to cancel out -3.

Practice Quiz

Test your knowledge with interactive questions

Solve for $$ b $$ :

$$ 8-b=6 $$

FAQ

Everything you need to know about this question

Why do I add 3 when the equation shows -3?

You add 3 because it's the opposite operation that cancels out -3. Think of it as: -3 + 3 = 0, which eliminates the constant from the left side completely.

What if I accidentally subtract 3 from both sides?

You'll get $x = -11$ , which is wrong! Always check by substituting back: $-3 + (-11) = -14 \neq -8$ . When you see your check doesn't work, try the opposite operation.

How do I remember which operation to use?

Use the opposite operation to cancel out constants. If you see +5, subtract 5. If you see -3, add 3. The goal is always to make the constant disappear by getting zero.

Can I move -3 to the right side instead?

Yes! Moving -3 to the right side gives: $x = -8 - (-3) = -8 + 3 = -5$ . This is the same as adding 3 to both sides, just thinking about it differently.

What does 'isolate the variable' actually mean?

Isolating the variable means getting the letter (like x) by itself on one side of the equation. You want: $x = \text{some number}$ , with nothing else attached to x.

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