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Practice Problem #1: Matching

Match the correct inequality with its expression.

Inequality:

  1. n > 1
  2. a ≥ 0
  3. f > −3
  4. −2 ≥ x
  5. x > −2

Expressions:

  • all real numbers greater than −3
  • all real numbers greater than −2
  • all real numbers greater than or equal to 0
  • all real numbers less than or equal to −2
  • all real numbers greater than 1

Answers:

  1. n > 1

    Answer: all real numbers greater than 1

  2. a ≥ 0

    Answer: all real numbers greater than or equal to 0

  3. f > −3

    Answer: all real numbers greater than −3

  4. −2 ≥ x

    Answer: all real numbers less than or equal to −2

  5. x > −2

    Answer: all real numbers greater than −2

Practice Problems #2-6: Multiple Choice

Choose the number that is included in the inequality.

  1. n < 4
    1. 4
    2. −4

    Answer: b. −4

  2. x ≥ 5.5
    1. 5.5
    2. 5.4

    Answer: a. 5.5

  3. c > ½
    1. 1
    2. −½

    Answer: a. 1

  4. a < 0
    1. 0
    2. −3

    Answer: b. −3

  5. −2 > x
    1. 2
    2. −4

    Answer: b. −4

Practice Problems #7: Guided Practice

In your notebook, graph the following inequality: a < −2

  1. Construct a number line. Make sure to include the isolated number in the middle of the number line.
    number line from negative 5 to zero
  2. Do you need an open circle or closed circle?
    open circle or closed circle
  3. Place the circle on the correct number.
    number line from negative 5 to zero with an open circle on negative 2
  4. Draw an arrow to the left, as all numbers less than −2 are to the left.
    number line from negative 5 to zero with an open circle on negative 2 and an arrow from the open circle pointing left

Practice Problems #8: Guided Practice

Solve the inequality n − 8 > 10. Start by adding 8 to both sides of the inequality.

n > ___blank

Answer: n > 18

When you add 8 to both sides of the inequality, you get n > 18.

Graph the inequality n − 8 > 10.

n > 18

  1. number line from positive 15 to positive 22. Closed circle at 18 with a line shaded to the left of the closed circle ending in an arrow to the left
  2. number line from positive 15 to positive 22. Closed circle at 18 with a line shaded to the right of the closed circle ending in an arrow to the right
  3. number line from positive 15 to positive 22. Open circle at 18 with a line shaded to the left of the open circle ending in an arrow to the left
  4. number line from positive 15 to positive 22. Open circle at 18 with a line shaded to the right of the open circle ending in an arrow to the right

Answer:

number line from positive 15 to positive 22. Open circle at 18 with a line shaded to the right of the open circle ending in an arrow to the right

Graph D is correct. You have an open point on our graph because your answer is n is "greater than" to 18. Shade to the right of 18 because these are the values that are true.

Practice Problems #9: Guided Practice

Solve the inequality −14 ≥ m − 12. Begin by rewriting the inequality by applying the symmetric property. Then, isolate the variable.

m ≤ ___blank

Answer: m ≤ −2

When you rewrite the inequality, you find that m − 12 ≤ −14. Then, add 12 to both sides to get m ≤ −2.

  1. number line negative 30 to negative 22. Open circle at negative 26 with a line shaded to the left of the open circle ending in an arrow to the left.
  2. number line negative 5 to positive 3. Closed circle at negative 2 with a line shaded to the left of the closed circle and ending in an arrow to the left
  3. number line negative 5 to positive 3. Open circle at negative 2 with a line shaded to the left of the open circle and ending in an arrow to the left
  4. number line negative 30 to negative 22. Closed circle at negative 26 with a line shaded to the left of the closed circle ending in an arrow to the left

Answer:

number line negative 5 to positive 3. Closed circle at negative 2 with a line shaded to the left of the closed circle and ending in an arrow to the left

Graph B is correct. The graph of m ≤ −2 will have a closed point and will be shaded to the left since we have "less than or equal to".

Practice Problems #10: Guided Practice

Solve the inequality −16x < 80. You will need to divide on both sides. Remember the rule for when you are multiplying or dividing by a negative number.

x > ___blank

Answer: x > −5

You should divide both sides by −16. Remember to flip your sign because you divided by a negative number.

  1. number line negative 8 to positive 2. Open circle at negative 5 with a line shaded to the right ending in an arrow to the right
  2. number line negative 8 to positive 2. Closed circle at negative 5 with a line shaded to the left ending in an arrow to the left
  3. number line negative 8 to positive 2. Open circle at negative 5 with a line shaded to the left ending in an arrow to the left
  4. number line negative 8 to positive 2. Closed circle at negative 5 with a line shaded to the right ending in an arrow to the right

Answer:

number line negative 8 to positive 2. Open circle at negative 5 with a line shaded to the right ending in an arrow to the right

Graph A is correct. The graph of x > −5 will have an open point and will be shaded to the right.

Practice Problems #11: Guided Practice

Solve the inequality:

fraction a over 2 is less than negative 12

You will not have to apply the symmetric property because the variable is already on the left side. Simply multiply by 2 on both sides of the equation.

a < ___blank

Answer: a < −24

After multiplying on both sides by 2, you have a < −24. You will not change the sign because you did not multiply by a negative number.

Answer: a < −24

  1. number line from negative 28 to negative 20. Closed circle at negative 24 and a line shaded to the right ending in an arrow pointing right
  2. number line from negative 28 to negative 20. Open circle at negative 24 and a line shaded to the left ending in an arrow pointing left
  3. number line from negative 28 to negative 20. Closed circle at negative 24 and a line shaded to the left ending in an arrow pointing left
  4. number line from negative 28 to negative 20. Open circle at negative 24 and a line shaded to the right ending in an arrow pointing right

Answer:

number line from negative 28 to negative 20. Open circle at negative 24 and a line shaded to the left ending in an arrow pointing left

Graph B is correct. The graph of a < −24 will have an open circle and will be shaded to the left.

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