Inequalities Part 1

Inequalities Part 1

You will likely want some paper and a pencil for this one!

Solution Sets

• The set of correct values for the variable is called a solution set

• You can use substitution to check to see if numbers in a set are true solutions

• Which numbers in the set $\left\{-8,\ -7,\ -6\right\}$   are solutions for the inequality  $3x\ge-21$  ?

•  $3\left(-8\right)\ ?\ge?\ -21\ \ \ \ is\ \ -24\ge-21\ \ is\ NOT\ TRUE$  

•  $3\left(-7\right)\ ?\ge?\ -21\ \ \ \ is\ \ -21\ge-21\ \ is\ TRUE$  

•  $3\left(-6\right)\ ?\ge?\ -21\ \ \ \ is\ \ -18\ge-21\ \ is\ TRUE$  
  

• Thus, the numbers from the set that are soltuions are -7 and -6.

Multiple Choice

Which numbers are solutions to x < 8?

• 8.6, 7.9, 7.7, -3.4

• 8, 10.4, 11, 16

• 0.8, 7.9, -4, 1.3

• 12, 7.1, 7.6, 4

Multiple Choice

Which set of numbers are solutions to this inequality?

 $9x\ \ge\ 45$  

• {5, 6, 7, 8}

• {2, 3, 4, 5}

• {4, 5, 6, 7}
  

• {4.8, 4.9, 5, 6}

Multiple Select

Which numbers are solutions to this inequality?

 $\frac{x+5}{2}<-2$  
Hint: There will only be two correct solutions shown. Be careful with comparing negative numbers!

• -10

• -9.5

• -9

• -8.5

• -8

Graphing Solutions

If the inequality has a line underneath it (an -or-equal-to inequality like  $\ge\ or\ \le$  ) then you shade the dot.

If the inequality does NOT have the line underneath it ( $>\ or\ <$  ) then you do NOT shade the dot.

Multiple Choice

When graphing do you use an open or closed circle for > ?

• Open (unshaded)

• Closed (shaded)

Multiple Choice

When graphing do you use an open or closed circle for  $\le$   ?

• Open (unshaded)

• Closed (shaded)

Multiple Choice

Match the graph with the given solution.

• A

• B

• C

• D

Multiple Choice

What inequality does the number line graph represent?

• x≥ 3

• x > 3

• x < -3

• x ≤ 3

Multiple Choice

What inequality does the number line graph represent

• x ≤ 4

• x ≥ -4

• x < -4

• x < 4

Multiple Choice

Which graph matches the inequality

½ ≤ a?

Hint: Rewrite this inequality with the a on the left by flipping it around.

• A

• B

• C

• D

Multiple Choice

Which graph matches the inequality

r ≥ -6?

• A

• B

• C

• D

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

Which inequality statement matches this graph?

• x < -13

• x < 13

• x > 13

• x > 13

Multiple Choice

Which inequality statement matches this graph?

• x > 5

• x < 5

• x < 5

• x > 5

Multiple Choice

What inequality does the number line graph represent?

• x ≥ 3

• x > 3

• x < -3

• x ≤ -3

Multiple Choice

Which inequality matches the graph?

• A

• B

• C

• D

Multiple Choice

Pick the correct inequality.

• A

• B

• C

• D

Solving Inequalities

• You can add/subtract a positive or negative number on both sides without affecting the inequality symbol.

• You can multiply or divide a positive number to both sides without affecting the inequality symbol.

• Just be careful, because multiplying/dividing by a negative number has an effect on the symbol!

Multiple Choice

Solve the inequality:

 $4h\ \le32$  
Treat it like an equation, undoing operations by doing a step to each side until the x is isolated on one side alone.

•  $h\le8$  

•  $h\ge8$  
  

•  $h\le128$  

•  $h\ge128$  

Multiple Choice

Solve and graph the solution:

k - 13 > -51

Treat it like an equation, undoing operations by doing a step to each side until the x is isolated on one side alone.

• A

• B

• C

• D

Multiple Choice

Solve and graph the solution:

p - 3 > -8

Treat it like an equation, undoing operations by doing a step to each side until the x is isolated on one side alone.

• A

• B

• C

• D

Multiple Choice

Solve:

5 < x + 3

Treat it like an equation, undoing operations by doing a step to each side until the x is isolated on one side alone.

• 2 > x

• 2 < x

• 8 > x

• 8 < x

Multiple Choice

Solve:

x + 5 > 10

Treat it like an equation, undoing operations by doing a step to each side until the x is isolated on one side alone.

• x < 15

• x < 5

• x > 15

• x > 5

Multiple Choice

Find the solution

• $X\ge4$

• $X\le4$

• $X\ \le\ 10$

• $X\ >\ 4$

Multiple Choice

3x - 2 < 13

• x > 3.67

• x > 5

• x < 5

• x < 3.67

Multiple Choice

6x - 4 ≥ 26

• x ≥ 3.67

• x ≥ 5

• x < 5

• x ≤ 5

Multiple Choice

4x - 10 ≤ 22

• x ≤ 8

• x ≥ 8

• x ≤ 3

• x ≥ 3