Inequality Review

Solving & Graphing Inequalities (One Step)

INEQUALITY DEFINTION

GREATER THAN

• is greater than

• is more than

LESS THAN

• is less than

• is fewer than

GREATER THAN OR EQUAL TO

• is greater than or equal to

• is at least

• is no less than

LESS THAN OR EQUAL TO

• is less than or equal to

• is at most

• is no more than

Inequalities Symbols Summary

Multiple Choice

What does the inequality sign mean?

• greater than

• less than

• greater than or equal to

• less than or equal to

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

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• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

What does the inequality sign mean?

• greater than

• less than

• greater than or equal to

• less than or equal to

Multiple Choice

Greater than or equal to

• <

• >

• ≤

• ≥

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I need at least 30 orders to meet my qouta.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I see more than a dozen seagulls.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

Greater than

• <

• >

• ≤

• ≥

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I can spend no more than $20 at the store.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

Less than or equal to

• <

• >

• ≤

• ≥

• Open Circles- Use when there is NOT a line under the inequality symbol

• Closed Circles- Use when there IS a line

Graphing Symbols

Multiple Choice

When graphing an inequality, you use an OPEN dot when you use which symbol?

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Choice

When you graph an inequality, you used a CLOSED dot when you use which symbols?

• ≤, ≥ 
• <, >
• ≤, <
• ≥, >

If the x is one the left side of the inequality, you can graph following the arrow rule!

Graphing Inequalities

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

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

Which graph matches the inequality
k < 3?

• A
• B
• C
• D

Solving Inequalities

​Example 1

​1. Remember we want X BY ITSELF
2. Subtract 3 from both sides

​3. Open circle at 1

​4. Arrow to the right

Multiple Choice

x + 5 > 7

• x > -2
• x > 2
• x > 12
• x > -12

​Example 2

​1. Add 3 to both sides

​2. Switch so the variable is on

​ the left side

​3. Closed circle at 3

​4. Arrow to the left

Multiple Choice

r - 14 ≥ 17

• r ≥ 3
• r ≥ -31
• r ≥ 31
• r ≥ -3

• Since the operation in the inequality is division, we will use multiplication to solve.

• Multiply both sides of the inequality sign by 5.

• 4 times 5=20

• x>20

• If we were to graph this, the circle would be open!

Multiple Choice

Solve

• x<4

• x≤1

• x≤4

• x≥1

Multiple Choice

Solve

• z≤1

• z>9

• z≤9

• z<9

​Example 3

​1. Divide both sides by 6

​2. Open circle at -4

​3. Arrow to the left

Multiple Choice

8x < 48

• x < -6
• x > -6
• x < 6
• x > 6

Multiple Choice

$$6x>12$$  

• $$x<2$$  

• $$x\le2$$  

• $$x>2$$  

• $$x\ge2$$  

​Example 4

​1. Divide both sides by -5

2. Flip the inequality sign!!!​

3. Closed circle at 2

​4. Arrow to the left

Multiple Choice

Solve the inequality

• -4 ≥ g

• 4 ≤ g

• 4 ≥ g

• 4 > g

Multiple Choice

When do you "flip the inequalities sign"?

• When you add or subtract a negative

• When it's a 1-step problem

• When you multiply or divide a negative

• When it's a 2-step problem

Multiple Choice

When do you flip the sign of an inequality?

• When ONLY multiplying by a negative

• When ONLY dividing by a negative

• BOTH multiplying or dividing by a negative

• Just do it when Ms. Bee tells you to

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Fill in the Blank

When you MULTIPLY or DIVIDE by a negative number on both sides of an inequality, you have to ______ the sign.

Multiple Choice

Solve the following inequality!

  $$-3z\ \ge\ 15$$  

• $$z\ge5$$  

• $$z\le5$$  

• $$z\ge-5$$  

• $$z\le-5$$  

Multiple Choice

Solve the following inequality!

$$-5c\ \le\ 30$$  

• $$c\ \ge\ -6$$  

• $$c\ \le\ -6$$  

Multiple Choice

s + 9 ≥ -25

• s ≥ -18
• s ≥ -34
• s ≤ 18
• s ≥ 34

Multiple Choice

10 ≥ x - 3

• x ≤ 13
• x ≥ 13
• x ≤ 7
• x ≥ 7