Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Algebra 1 · Chapter 1 · Lesson 5

Practice Worksheet

No Solution, or Every Solution

When the x disappears, read what is left.

11 problems · about 20 minutes · A-REI.B.3

NameDate

Figure — use these to answer the problems

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

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. 8x + 2 = 8x + 11. How many solutions?

    Answer

  2. 2x + 5 = 2x + 5. How many solutions? Use 99 for infinitely many.

    Answer

  3. 7x + 1 = 7x + 4. How many solutions?

    Answer

  4. 4x = 4x. How many solutions? Use 99 for infinitely many.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 3x + 2 = 5x + 2. What is x?

    Answer

  2. Sort each result by what it means.

    Write each item under the heading it belongs to: x = 4 · 3 = 8 · 6 = 6

    Exactly one solution

    No solution

    Every number

  3. Two lines with the same slope and different intercepts. How many solutions?

    Answer

Stretch Yourself

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

4 problems

  1. 2(x + 4) = 2x + 8. How many solutions? Use 99 for infinitely many.

    Answer

  2. 6x + 3 = 6x − 3. How many solutions?

    Answer

  3. The Contradiction

    3x + 2 = 3x + 8. How many solutions?

    Answer

  4. The Identity

    5(x + 2) = 5x + 10. Is every number a solution? 1 for yes, 0 for no.

    Answer