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Cogito

Algebra 1 · Chapter 2 · Lesson 1

Practice Worksheet

Solving Inequalities

One rule is different, and it matters.

10 problems · about 19 minutes · A-REI.B.3

NameDate

Figure — use these to answer the problems

Multiplying by a negative flips a number across zero, and it flips the order too.
-10-8-6-4-20246810flip about 03-3
3 × -1 = -3
Number3
Multiply by-1
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Absolute Value Equations”

    |x − 4| = 3. What is the larger solution?

    Answer

  2. From “No Solution, or Every Solution”

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

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Solve −2x ≥ 14. Boundary value?

    Answer

  2. Why does the sign reverse with a negative?

    • Multiplying by a negative reverses the order on the line.
    • Because that is the rule.

  3. Solve 2x − 3 > 7. Boundary value?

    Answer

  4. Solve −3x < 12. Boundary value?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. Solve 5x + 2 ≤ 27. Boundary value?

    Answer

  2. Does dividing by a positive reverse the sign?

    • No. Only a negative does.
    • Yes.

Stretch Yourself

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

2 problems

  1. The Range

    Solve 3x + 4 < 19. What is the boundary value of x?

    Answer

  2. The Flip

    Solve −4x > 20. What is the boundary value of x?

    Answer