Solve the Linear Equation: Find X in -8 - x = -5

Linear Equations with Negative Constants

Solve for X:

8x=5 -8-x=-5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Isolate the unknown X
00:21 Reduce what we can
00:29 Convert from negative to positive
00:39 Negative times negative always equals positive
00:44 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

8x=5 -8-x=-5

2

Step-by-step solution

To solve the equation 8x=5 -8 - x = -5 , we'll isolate the variable x x by performing algebraic operations:

Step 1: Add 8 to both sides of the equation to eliminate the 8-8:

8x+8=5+8 -8 - x + 8 = -5 + 8

This simplifies to:

x=3 -x = 3

Step 2: To solve for x x , we need to change the sign of x x . Multiply both sides by 1-1:

x=3 x = -3

Therefore, the solution to the equation is 3\boxed{-3}.

3

Final Answer

3 -3

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Move all constants to one side systematically
  • Technique: Add 8 to both sides: -8 - x + 8 = -5 + 8
  • Check: Substitute x = -3: -8 - (-3) = -8 + 3 = -5 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to change signs when moving terms
    Don't subtract 8 from both sides when you see -8 - x = wrong answer! This makes the equation -16 - x = -13. Always add the opposite: if you see -8, add +8 to both sides.

Practice Quiz

Test your knowledge with interactive questions

\( 11=a-16 \)

\( a=\text{?} \)

FAQ

Everything you need to know about this question

Why do I add 8 instead of subtract 8?

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When you see 8x=5 -8 - x = -5 , you want to eliminate the -8. To cancel out -8, you add +8 (because -8 + 8 = 0). Think of it as undoing the -8!

What does multiplying by -1 actually do?

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Multiplying by -1 flips the sign of every term. So x=3 -x = 3 becomes x=3 x = -3 . It's like taking the opposite of both sides!

How can I check if x = -3 is really correct?

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Substitute x = -3 back into the original equation: 8(3)=8+3=5 -8 - (-3) = -8 + 3 = -5 . Since this equals -5, our answer is correct!

Why is the answer negative when we're adding?

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The answer x = -3 comes from x=3 -x = 3 , not from adding. When we have negative x equals positive 3, then x must be negative to make this true!

What if I got x = 3 instead of x = -3?

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Check your work! If you got x = 3, you probably forgot the final step of multiplying by -1. Remember: x=3 -x = 3 means x = -3, not x = 3.

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