Solving 2-step Inequalities

​Two Step Inequalities

​Solving Two Step Inequalities

• The variable must be alone or isolated on one side of the inequality.

• Isolate the variable by using inverse or opposite operations. ​

• Whatever you do to one side ​you must do to the other.

​1) add or subtract - whatever the inverse is of the constant

​2) multiply or divide - whatever the inverse operation is of the coefficient

Multiple Choice

What is the opposite of multiplication?

• Addition

• Subtraction

• Division

Multiple Choice

What is the opposite of addition?

• Subtraction

• Multiplication

• Division

Multiple Choice

What would a graph look like for this solution:

x > 10

• Open circle; shaded to the right

• Open circle; shaded to the left

• Closed circle; shaded to the right

• Closed circle; shaded to the left

Multiple Choice

What would the graph look like for your solution?

x < 50

• Open circle; shaded to the right

• Closed circle; shaded to the right

• Closed circle; shaded to the left

• Open circle; shaded to the left

Multiple Choice

$$x\ \ge\ -5$$  

What would the graph look like for your solution?

• Closed circle; shaded to the left

• Closed circle: shaded to the right

• Open circle; shaded to the right

• Open circle; shaded to the left

Multiple Choice

When graphing an inequality, you use a closed circle when you use which symbols?

• ≤, ≥

• <, >

Multiple Choice

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

• <, >

• ≤, ≥ 

Multiple Choice

What inequality does the number line graph represent?

• $$x\le-4$$  

• $$x\ge-4$$  

• x < -4

• x < 4

Multiple Choice

What inequality does the number line graph represent?

• $$x\ge3$$  

• x > 3

• x < -3

• $$x\le3$$  

​Two Step Inequalities

​Solving Two Step Inequalities

• When you multiply or divide BY a negative number, the inequality sign is flipped.

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

Multiple Choice

Does the sign need to flip when solving?
-2x ≥ 22

• YES

• NO

Multiple Choice

Do I need to flip my sign?
3x  ≥ 12

• Yes

• No

Multiple Choice

Solve for t.

6t + 4 ≤ -2

• t ≤ -1 

• t ≤ 1

• t=1

• 1=t

Multiple Choice

Solve for k. 

7k – 2 ≥ -9

• k ≤ -1

• k≤1

• k≥1

• k ≥ -1

Multiple Choice

Solve for u. 
u/7 – 1 ≤ 1

• 14≥u

• 14≤u

• u≤14

• u ≤ -14

Multiple Choice

-3y + 2 > 11

• y < -3

• y > -3

• y < 3

• y > 3

Multiple Choice

22 < 6c + 4

• 11>c

• 3>c

• 11<c

• 3<c