Solve for X in the Linear Equation: 9 - x = 16 - 7

Linear Equations with Simplified Right Side

Solve for X:

9x=167 9 - x = 16 - 7

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1

Understand the problem

Solve for X:

9x=167 9 - x = 16 - 7

2

Step-by-step solution

First, simplify the right side of the equation:
167=9 16 - 7 = 9
Hence, the equation becomes 9x=9 9 - x = 9 .
Since both sides are equal, x x must be 0 0 .
Therefore, the solution is x=0 x = 0 .

3

Final Answer

0

Key Points to Remember

Essential concepts to master this topic
  • Simplification Rule: Always simplify both sides before solving for the variable
  • Technique: Calculate 167=9 16 - 7 = 9 to get 9x=9 9 - x = 9
  • Check: Substitute x = 0: 90=9 9 - 0 = 9 equals 167=9 16 - 7 = 9

Common Mistakes

Avoid these frequent errors
  • Solving without simplifying the right side first
    Don't try to solve 9x=167 9 - x = 16 - 7 by moving terms around before simplifying = confusion and errors! This makes the problem unnecessarily complicated. Always simplify each side completely before isolating the variable.

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 16 - 7 first?

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Simplifying first makes the equation clearer! When you see 9x=9 9 - x = 9 , it's obvious that x must be 0. If you don't simplify, you might make calculation errors.

How do I know when both sides are equal?

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When you have the same number on both sides (like 9 = 9), the variable that makes this true is your answer. In 9x=9 9 - x = 9 , x must be 0.

What if I got x = -2 instead?

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Check your work! If x = -2, then 9(2)=9+2=11 9 - (-2) = 9 + 2 = 11 , but 167=9 16 - 7 = 9 . Since 11 ≠ 9, x = -2 is wrong.

Can I solve this by moving terms to one side?

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Yes, but it's easier to simplify first! You could write 9x16+7=0 9 - x - 16 + 7 = 0 , but that creates 0x=0 0 - x = 0 , giving the same answer with more steps.

What does it mean when x = 0?

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It means zero is the solution! When you substitute 0 for x in the original equation, both sides become equal. Zero is a perfectly valid answer in algebra.

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