M5&6 Rew Equations and Inequalitiesevi

By the end of this lesson you will be able to solve linear equations that require distribution

Steps:

• Distribute wherever there are parantheses

• Combine like terms on each side of the equation

• Inverse Operations to solve for the variable

• Check your work

Example: Solve the equation

4(3x - 5) = 52

Steps:

• distribute
• solve using inverse operations
• check your work

Step 1: Distribute wherever necessary

4(3x - 5) = 52

Step 2: Solve Using Inverse Operations

12x - 20 = 52

-  Add 20 to both sides

12x = 72

- Divide both sides by 12
x = 6

Step 3: Check x = 6

4 (3*6 - 5 ) = 52

4(18 - 5) = 52

4(13) = 52

52 = 52 CHECKS!

Multiple Choice

Distribute:

4(x+2)

• 4x+8

• 4x+2

• $$\frac{x+2}{4}$$

• 8x

Multiple Choice

Distribute:

-2(x+1)

• -2x

• -2x+1

• -2x+2

• -2x-2

Multiple Choice

Solve:

2(x+1) = 6

• x = -1

• x = 4

• x = 2

• x = -2

Multiple Choice

Solve:

-2(x-1) = 6

• x = 2

• x = -2

• x = 4

• x = -4

Multiple Choice

4( x + 2) = 16

What is the solution to the equation?

• -2

• 0

• 1

• 2

2-Step Equations

How to Solve!

Get rid of the 3rd Wheel: Add or Subtract to get rid of the number

Break up the happy couple: Multiply or Divide both sides of the equation by the coefficient

Multiple Choice

What is the first step to solving the equation

$$-2x-15=-27$$  ?

• add 15 to both sides

• subtract 15 from both sides

• multiply both sides by 15

• divide both sides by 15

Fill in the Blanks

Multiple Choice

What is the next step to solve the equation

$$-2x=-12$$  ?

• add -2 to both sides of the equation

• subtract -2 from both sides of the equation

• multiply both sides of the equation by -2

• divide both sides of the equation by -2

Fill in the Blanks

Multiple Choice

How do you prove that your solution is correct? What is your success criteria for solving equations?

• I don't need to check: it's probably right!

• Substitution: plug the solution in for x and verify that the number sentence is true.

Multiple Choice

What is the first step to solving the equation

$$13+\frac{x}{-10}=-3$$  ?

• add 13 to both sides

• subtract 13 from both sides

• add 10 to both sides

• subtract 10 from both side

Fill in the Blanks

Multiple Choice

What is the next step to solve the equation

$$\frac{x}{-10}=-16$$  ?

• add 10 to both sides of the equation

• subtract 10 from both sides of the equation

• multiply both sides of the equation by -10

• divide both sides of the equation by -10

Fill in the Blanks

Multiple Choice

How do you prove that your solution is correct? What is your success criteria for solving equations?

• I don't need to check: it's probably right!

• Substitution: plug the solution in for x and verify that the number sentence is true.

Solving One Step Inequalities

Multiple Choice

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

• ≤, ≥ 

• <, >

• ≤, <

• ≥, >

Multiple Choice

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

• ≤, ≥ 

• <, >

• ≤, <

• ≥, >

Multiple Choice

What inequality does the number line graph represent?

• x > 5
• x < −5
• x ≥ 5
• x ≥ −5

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

Solve the inequality.

$$n-5\ge\ 2$$  

• $$n\le7$$  

• $$n\ge3$$  

• $$n\ge7$$  

• $$n\le-3$$  

Multiple Choice

Solve the inequality.

$$5>n-3$$  

• $$8<n$$  

• $$8>n$$  

• $$2>n$$  

• $$2<n$$  

Multiple Select

When does the inequality sign change?

• When adding

• When multiplying

• When dividing by a negative

• When multiplying by a negative

• When subtracting

Multiple Choice

Solve the inequality.

$$-7y\le14$$  

• $$y\le-2$$  

• $$y\ge-2$$  

• $$y\le2$$  

• $$y\ge2$$