Solve for X in the Equation: 8 - x = 11 - 3

Linear Equations with Simplification Steps

Solve for X:

8x=113 8 - x = 11 - 3

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1

Understand the problem

Solve for X:

8x=113 8 - x = 11 - 3

2

Step-by-step solution

First, simplify the right side of the equation:
113=8 11 - 3 = 8
Hence, the equation becomes 8x=8 8 - x = 8 .
Subtract 8 from both sides to isolate x x :
8x8=88 8 - x - 8 = 8 - 8
This simplifies to:
x=0 -x=0
Divide by -1 to solve for x x :
x=0 x = 0
Therefore, the solution is x=0 x = 0 .

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify all arithmetic operations before isolating the variable
  • Technique: Calculate 11 - 3 = 8 first, creating 8 - x = 8
  • Check: Substitute x = 0 back: 8 - 0 = 8 and 11 - 3 = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to isolate x before simplifying the right side
    Don't work with 8 - x = 11 - 3 directly without calculating 11 - 3 first = makes algebra unnecessarily complex! This leads to confusion and errors with negative signs. Always simplify all arithmetic operations on both sides before isolating variables.

Practice Quiz

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\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I need to simplify 11 - 3 first?

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Simplifying arithmetic first makes the equation much cleaner to work with! Instead of dealing with 8x=113 8 - x = 11 - 3 , you get the simpler 8x=8 8 - x = 8 .

What if both sides have the same number like 8 = 8?

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When you get the same number on both sides after simplification, it means the variable equals zero! In 8x=8 8 - x = 8 , subtract 8 from both sides to get x=0 -x = 0 , so x=0 x = 0 .

Why do I divide by -1 at the end?

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Because you have x=0 -x = 0 , not x=0 x = 0 . The negative sign means negative x equals zero, so dividing both sides by -1 gives you x=0 x = 0 .

How can I check if x = 0 is really correct?

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Substitute x = 0 into the original equation: Left side is 8 - 0 = 8, right side is 11 - 3 = 8. Since 8 = 8 is true, your answer is correct!

What if I get confused with the negative signs?

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Take it step by step! From 8x=8 8 - x = 8 , subtract 8 from both sides to get x=0 -x = 0 . Then multiply both sides by -1 to get x=0 x = 0 . Go slowly and check each step!

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