2.2 Solving Advanced Linear Equations

Multiple Choice

What does Linear mean?

• Straight Line

• $$x^2$$

• Upside Down Line

• No clue

Multiple Choice

What does the Addition Properties of Equality said?

• I can add any number to linear equation

• I have to keep the equation balance

• I can add any number to an equation as long as I do it to both side of the equation

• No clue

Multiple Choice

What does the Distributive Property say?

(a + b)c =

• The distributive property is used to multiply a single term and two or more terms inside a set of parentheses.

  ac + bc

• The distributive property is used to add a single term and two or more terms inside a set of parentheses.

  a+c + b+c

• The distributive property is used to subtract a single term and two or more terms inside a set of parentheses.

  a-c + b-c

Multiple Choice

To cancel out a multiplicative we need to find the multiplicative inverse or reciprocal. What is the reciprocal of $$\frac{2}{5}$$ ?

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$5\left(2\right)$$

Multiple Choice

Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% or .75 of them. Zach attempted 10 more shots than Jared did and made 80% or .80 of them. Together, they made a total of 101 shots. Which equation represents this situation?

• • 0.75x = 0.8(x + 10)

• • 0.75(x + 10) + 0.8x = 101

• • 0.75x + 0.8x + 10 = 101

• • 0.75x + 0.8(x + 10) = 101

Multiple Choice

What is the 1st step we need to do to solve 0.75x + 0.8(x + 10) = 101?

• Add like term

  0.75x +0.8x

• subtract 10 from both side

• Use the Distributive Property

  0.8(x) +0.8(10)

Multiple Choice

After use the Distributive Property we get

0.75x +0.8x + 8 = 101

What do we do next?

• subtract 8 from both side

• combine like term

  0.75x + 0.8x

Multiple Choice

After combine like terms we get

1.55x + 8 = 101

How do I cancel out the 8 or how do I get it to 0?

• Add 8 to both side

• subtract 8 from both side

• multiply 8 to both side

• divide 8 to both side

Multiple Choice

All most this!!

Now we have 1.55x = 93

Now what?

• Add 1.55 to both side

• subtract 1.55 to both side

• multiply 1.55 from both side

• divide 1.55 from both side

Multiple Choice

$$\frac{p+1}{2}=\frac{3p+7}{5}$$

What is the 1st step?

• Add p+1 +3p+7

• found common denominator

• cross multiply

Multiple Choice

After cross multiply, we do what next?

5(p + 1) = 2(3p + 7)

• Need to add 5 +2

• Use the distributive property to eliminate the parentheses

  5(p) + 5(1) = 2(3p) +2(7)

• combine like term

  p+3p

Multiple Choice

Apply the distributive property to eliminate the parentheses we get
5p + 5 = 6p + 14

How to I move the 5p to the other side?

• add 5p to both side

• subtract 5p from both side

• multiply 5p to both side

• divide 5p from both side

Multiple Choice

Use the properties of equality to isolate p:
5 = 1p + 14

how to I move the 14 to the other side or cancel it out?

• add 14 to both side

• subtract 14 from both side

• multiply 14 to both side

• divide 14 from both side

Multiple Choice

How many solutions does this equation have?

-1.7v +2.8 = 1.4v - 3.1v +2.8

-1.7v + 2.8 = -1.7v +2.8

2.8 = 2.8

• No solution

• One solution

• Infinitely

Multiple Choice

How many solutions does this equation have?

4a -3 +2a = 7a -2

6a - 3 = 7a - 2

-3 = a - 2

-1 = a

• No solution

• One Solution

• Infinitely

Multiple Choice

How many solutions does this equation have?

2y - 3 = 5 +2(y-1)

2y - 3 = 5 2y - 2

2y - 3 = 2y + 3

-3 = 3

• No Solution

• One Solution

• Infinitely

All done with this lesson. Time for a short Quiz