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Chess Club: Rating Equality Checks worksheet preview

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Chess Club: Rating Equality Checks

Classify chess club rating equations as having one solution, no solution, or infinitely many solutions using simplification.

Grade 8MathInteractive · Printable

Aligned to8.EE.C.7.a

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 14 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 8
Subject
Math
Question types
Fill in the blank, Multiple choice, Matching, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

  • Students simplify linear equations to identify one solution, no solution, or infinitely many solutions.
  • Students interpret identities and contradictions in hypothetical chess rating calculations.
  • Students use simplified equations to justify the number of solutions.

How to use

Use after introducing equations with variables on both sides. Ask students to show simplification on separate paper and discuss the final error analysis.

Curriculum

Common Core standard covered

8.EE.C.7.a

Show with examples that a linear equation in one variable can have one solution, infinitely many, or none, by simplifying it.

Preview

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Name Date

Chess Club: Rating Equality Checks

Simplify tournament equations to decide how many solutions they have.

Simplify the Rating Checks

These are hypothetical chess club calculations, not official rating rules. Variables represent real numbers. Simplify each equation before deciding how many solutions it has.

1.
Two tournament worksheets give the equation 3(x + 8) = 3x + 24. Which statement describes its solutions?
  • A. Only x = 0 makes the equation true.
  • B. Only x = 8 makes the equation true.
  • C. No real number makes the equation true.
  • D. Every real number makes the equation true.
2.
A rating check compares 5x + 18 and 5x + 26. What does simplifying 5x + 18 = 5x + 26 show?
  • A. It becomes x = 0, so there is one solution.
  • B. It becomes 18 = 26, so there is no solution.
  • C. It becomes x = 8, so there is one solution.
  • D. It becomes 0 = 0, so there are infinitely many solutions.
3.
The club compares two rating-adjustment expressions: 2(x + 15) = 3x + 18. Which conclusion is correct?
  • A. There is one solution: x = 12.
  • B. There are no solutions.
  • C. There are infinitely many solutions.
  • D. There is one solution: x = −12.

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