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Cogito

Grade 8 Math · Chapter 4 · Lesson 2

Practice Worksheet

None, One, or Infinitely Many

Not every equation has exactly one answer.

10 problems · about 18 minutes · 8.EE.C.7

NameDate

Figure — use these to answer the problems

Two lines with the same slope never meet, which is what "no solution" looks like.
-10-10-5-5551010
y = 2x + 3
Slope2
Intercept3
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Variables on Both Sides”

    Solve 7x + 3 = 4x + 18.

    Answer

  2. From “Comparing Lines in Different Forms”

    At x = 0, y = 8; at x = 5, y = 33. What is the slope?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. 7x + 2 = 7x + 9. How many solutions?

    • None.
    • Infinitely many.

  2. The variable vanishes and leaves a true statement. What does that mean?

    • Every value of x works.
    • No value works.

  3. 2x + 4 = 2x + 4. How many solutions?

    • Infinitely many.
    • None.

  4. 6x + 1 = 6x + 8. How many solutions?

    • None.
    • Infinitely many.

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Solve 3x + 4 = x + 10.

    Answer

  2. 4(x + 1) = 4x + 4. How many solutions?

    • Infinitely many.
    • None.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Collapse

    3x + 2 = 3x + 9 leaves 2 = 9. How many solutions?

    Answer

  2. The Identity

    5(x + 2) = 5x + 10 leaves 10 = 10. Does every value of x work?

    • Yes. Infinitely many solutions.
    • No.