Check for Balance: Are the Equations 9-x=1 and 5x=-40 Equal?

Equation Balancing with Different Solutions

Are the equations balanced?

9−x=1=?5x=−40 9-x=1\stackrel{?}{=}5x=-40

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1

Understand the problem

Are the equations balanced?

9−x=1=?5x=−40 9-x=1\stackrel{?}{=}5x=-40

2

Step-by-step solution

To determine if the two equations are balanced, we need to evaluate them separately:

First, we solve the equation 9−x=19 - x = 1.

  • Subtract 9 from both sides to isolate −x-x:
  • −x=1−9-x = 1 - 9
  • −x=−8-x = -8
  • Multiply both sides by −1-1 to solve for xx:
  • x=8x = 8

Next, we solve the equation 5x=−405x = -40.

  • Divide both sides by 5 to isolate xx:
  • x=−405x = \frac{-40}{5}
  • x=−8x = -8

The solution to the first equation is x=8x = 8 and the solution to the second equation is x=−8x = -8. Since the solutions for xx are not the same, the two equations are not balanced.

Therefore, the correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Balance Check: Two equations are balanced only if they have identical solutions
  • Technique: Solve each equation separately: 9−x=19-x=1 gives x=8x=8, 5x=−405x=-40 gives x=−8x=-8
  • Verification: Compare solutions: x=8x=8 ≠ x=−8x=-8, so equations are not balanced ✓

Common Mistakes

Avoid these frequent errors
  • Assuming equations are balanced without solving
    Don't just look at the equations and guess they're balanced = wrong answer! The equations might look related but have completely different solutions. Always solve each equation separately and compare the x-values.

Practice Quiz

Test your knowledge with interactive questions

Are the equations balanced?

\( 9-x=1\stackrel{?}{=}5x=-40 \)

FAQ

Everything you need to know about this question

What does it mean for equations to be 'balanced'?

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Two equations are balanced when they have the exact same solution. It's like asking if x=8x = 8 and x=−8x = -8 are the same - they're clearly not!

Do I need to solve both equations completely?

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Yes! You must find the value of x in both equations. Only then can you compare whether the solutions are identical or different.

What if I made an algebra mistake while solving?

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Always check your work by substituting your answer back into the original equation. For example, if x=8x = 8, then 9−8=19 - 8 = 1 ✓

Can equations look different but still be balanced?

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Absolutely! Equations like 2x=102x = 10 and x+3=8x + 3 = 8 look different but both have x=5x = 5, so they're balanced.

What's the quickest way to check if equations are balanced?

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Solve each equation for x, then compare the values. If they're the same, the equations are balanced. If different, they're not balanced - it's that simple!

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