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3D-Printing Club: Do the Designs Agree? worksheet preview

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3D-Printing Club: Do the Designs Agree?

Use 3D-printing design checks to distinguish linear equations with one solution, no solution, or infinitely many solutions.

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
  • 13 questions
  • Classroom-ready

Details

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

About this worksheet

What students practice

  • Students simplify linear equations to identify one solution, no solution, or infinitely many solutions.
  • Students use simplified equations to justify when two design expressions are equal.

How to use

Have students simplify each equation before choosing an answer. Discuss why a true constant statement and a false constant statement lead to different conclusions.

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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3D-Printing Club: Do the Designs Agree?

Simplify equations to determine how many solutions they have.

Design File Checks

Treat x as any real number unless a problem states otherwise. Simplify both sides before deciding how many solutions an equation has.

1.
The club checks three equations saved in design files. Match each equation to its simplified form after distributing and combining like terms on each side.
  1. 2(3x − 4) + x = 7x − 8
  2. 3(x + 5) − x = 2x + 12
  3. 4(x − 2) + x = 3x + 6
  1. A. 7x − 8 = 7x − 8
  2. B. 5x − 8 = 3x + 6
  3. C. 2x + 15 = 2x + 12
2.
A design check uses −3(2x − 5) + x = 15 − 5x. Which conclusion follows from simplifying?
  • A. It has one solution because it simplifies to x = 3.
  • B. It has infinitely many solutions because it simplifies to 15 = 15.
  • C. It has one solution because it simplifies to x = 0.
  • D. It has no solution because it simplifies to 15 = −15.
3.
A scaling check uses 0.4(5x + 10) = 3x + 1. Its simplified equation has exactly one solution. Find it.

x =  

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