Lesson 5

Efficiently Solving Inequalities

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Problem 1

  1. Consider the inequality \(\text-1 \leq \frac{x}{2}\).
    1. Predict which values of \(x\) will make the inequality true.
    2. Complete the table to check your prediction.
      \(x\) -4 -3 -2 -1 0 1 2 3 4
      \(\frac{x}{2}\)
  2. Consider the inequality \(1 \leq \frac {\text{-}x}{2}\).
    1. Predict which values of \(x\) will make it true.
    2. Complete the table to check your prediction.
      \(x\) -4 -3 -2 -1 0 1 2 3 4
      \(\text-\frac{x}{2}\)

Solution

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Problem 2

Diego is solving the inequality \(100-3x \ge \text-50\). He solves the equation \(100-3x = \text-50\) and gets \(x=50\). What is the solution to the inequality?

A:

\(x < 50\)

B:

\(x \le 50\)

C:

\(x > 50\)

D:

\(x \ge 50\)

Solution

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Problem 3

Solve the inequality \(\text-5(x-1)>\text-40\), and graph the solution on a number line.

Solution

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Problem 4

Select all values of \(x\) that make the inequality \(\text-x+6\ge10\) true.

A:

-3.9

B:

4

C:

-4.01

D:

-4

E:

4.01

F:

3.9

G:

0

H:

-7

Solution

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(From Unit 4, Lesson 3.)

Problem 5

Draw the solution set for each of the following inequalities.

  1. \(x>7\)

    A number line with the numbers negative 10 through 9 indicated.

  2. \(x\geq\text-4.2\)

    A number line with the numbers negative 10 through 9 indicated.

Solution

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(From Unit 4, Lesson 3.)