Two-Step Equations and Inequalities Review

Two Step Equations

Our Goal

• Isolate the variable on one side of the equal sign

Multiple Choice

What does isolate the variable mean?

• Get the variable alone

• Get rid of the variable

Our Strategy

• Keep it balanced

• What you do to one side, do to the other

• "Copy and Paste"

Use Inverse Operations to isolate the variable

• Inverse of addition - subtraction

• Inverse of subtraction - addition

• Inverse of multiplication - division

• Inverse of division - multiplication

Multiple Choice

What is the inverse of multiplication?

• Addition

• Subtraction

• Multiplication

• Division

3x - 6 = 12

• Add 6 to both sides: 3x = 18

• Divide both sides by 3: x = 6

• Check: 3(6) - 6 = 18 - 6 = 12

Multiple Choice

12g - 5 = 19

Which is the correct 1st step?

• Add 12 to both sides

• Add 5 to both sides

• Add 19 to both sides

Multiple Choice

$$12g-5=19$$  

$$\ \ \ \ \ \ \ +5\ \ \ \ +5\ \ \ \ \ \ \ \$$   $$12g\ \ \ \ \ \ \ =\ 24$$   What is the next step?

• Multiply both sides by 12

• Divide both sides by 12

• Multiply both sides by 24

• Divide both sides by 24

Multiple Choice

2t -7 = 3

Find the value of t

• -2

• 2

• 5

• 20

Multiple Choice

10 = 2d - 5

What is the value of d?

• 2.5

• 7.5

• 15

• 20

Multiple Choice

$$3x+2\ =\ -25$$  

• $$x\ =\ -8$$  

• $$x\ =\ -9$$  

• $$x\ =\ 9$$  

• $$x\ =\ 24$$  

What is an inequality?

Inequality means "not equal"

**Note** Inequalities does not contain the equal sign.

Multiple Choice

What does inequality mean?

• equal

• not equal

Multiple Choice

TRUE or FALSE: Inequalities contain equal signs.

• TRUE

• FASLE

Process Steps

• Step 1: Add or subtract like terms

• Step 2: Multiply or divide both sides by the coefficient (the # with the variable).

• **If the coefficient is negative, flip the inequality sign**

• Remember we want the variable on one side by itself!

• Step 3: Set the variable to the solution using the inequality symbol.

Multiple Choice

What is the solution set for

$$-8x+40>-16$$  ?

• $$x>7$$  

• $$x<7$$  

• $$x>-3$$  

• $$x<-3$$  

Multiple Choice

Do I need to flip my sign?
3x  ≥ 12

• Yes

• No

Multiple Choice

Do I need to flip my sign?
-3x  ≥ 12

• Yes

• No

Multiple Choice

When graphing b < 6 would you use an open or closed circle?

• Open

• closed

Multiple Choice

Solve and graph the inequality.
77 ≤ 5 + 8n

• A

• B

• C

• D

Multiple Choice

Solve and graph the inequality.
7n - 1 > 76

• A

• B

• C

• D

Multiple Choice

22 < 6c + 4

• 11>c

• 3>c

• 11<c

• 3<c

Multiple Choice

25 < X - 10

• X > 35

• X < 35

• X > -35

• X < -35

Multiple Choice

2- 3x ≤ 20

• x  ≥ -6

• x ≤ -6

• x ≤ -7

• x  ≥ -7

Multiple Choice

s + 9 ≥ -25

• s ≥ -18

• s ≥ -34

• s ≤ 18

• s ≥ 34