Lecture 2.1-2.4 - Writing & Solving Equations

2.1-2.4 - Writing & Solving Equations

This a lecture, take notes.

Hey. It's me, Mr. Geering. The lecture you are about to partake in is a replacement for my absence. Treat as if I was there meaning be quiet, respectful, and take notes for the examples. Because this is based in Quizizz, it is very easy to click through it. Don't. Take your time and learn the material.

Let's get this bread

Multiple Choice

Which of the following key words mean EQUALS TO

• Product

• Quotient

• Is

• Difference

Multiple Choice

Translate the following equation:

The product of 15 and a number is 45

• 15 + x = 45

• 15x = 45

• 15 - x = 45

• $$\frac{15}{x}=\ 45$$

Multiple Choice

Translate the following equation:

h + 30 = 60

• Thirty decrease by a number is 60

• The product of 30 and a number equals 60

• A number increased by 30 is equivalent to 60

• The quotient of a number and 30 is 60

Multiple Choice

Translate the following equation:

$$\frac{25}{s}=\ 5$$  

• The quotient of 25 and a number is equal to 5

• The product of 25 and a number is equal to 5

• Twenty-five decreased by a number is 5

• A number divided by 25 is 5

Multiple Choice

Translate the following equation:

Thirty decreased by a number is 12

• 30 + x = 12

• x - 30 = 12

• 30x = 12

• 30 - x = 12

Multiple Choice

Translate this sentence into an equation.

Twice the sum of a number and 3 is 20.

Use the variable x to represent the number.

• $$2x+3=20$$

• $$2x+3-10$$

• $$3\left(x+2\right)=20$$

• $$2\left(x+3\right)=20$$

Multiple Choice

Translate this phrase into an algebraic equation:

A number tripled subtracted from 60 is the same as 21.

• 3c − 60 = 21

• 60 − 3 = 21c

• 60 − 3c = 21

• c(60 − 3) = 21

Multiple Choice

Translate this phrase into an algebraic equation:

Six fewer than twice a number is four.

• 6 - 2x = 4

• 2x - 6 = 4

• x² - 6 = 4

• 6 - x² = 4

Audio Response

Translate the equation into a sentence:

$$6z-15=45$$  

Open Audio Recorder

Audio Response

Translate the equation into a sentence:

$$x^2+3x=10$$  

Open Audio Recorder

Properties of Equality

​"Whatever you do on one side, you have to do on the other side" - Mr. Geering nasally voice

Remember additive and multiplicative inverses? That's what you're doing.

1. Addition

2. Subtraction

3. Multiplication

4. Division​

Reorder

To solve the equation $$\frac{\left(5x-3\right)}{4}+2=12$$  reorder the following

• Subtract 2 from both sides

• Multiply both sides by 4

• Add 3 to both sides

• Divide both sides by 5

1

2

3

4

• 1
• 2
• 3
• 4

Reorder

To solve the equation $$4\left(\frac{x}{2}+3\right)+7=43$$ reorder the following

• Subtract 7 from both sides

• Divide both sides by 4

• Subtract 3 from both sides

• Multiply both sides by 2

1

2

3

4

• 1
• 2
• 3
• 4

Reorder

To solve the equation $$\frac{4\left(10+x\right)-5}{7}=42$$  reorder the following

• Multiply both sides by 7

• Add 5 to both sides

• Divide both sides by 4

• Subtract 10 from both sides

• D

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Reorder

To solve the equation $$\frac{\left(5x-8\right)}{3}=4$$   reorder the following

• Multiply both sides by 3

• Add 8 to both sides

• Divide both sides by 5

1

2

3

• 1
• 2
• 3

Reorder

To solve the equation $$\frac{\left(3-\frac{x}{2}\right)}{5}-4=12$$   reorder the following

• Add 4 to both sides

• Multiply both sides by 5

• Subtract 3 from both sides

• Multiply both sides by -2

1

2

3

4

• 1
• 2
• 3
• 4

Reorder

To solve the equation $$\frac{\left(12-3x\right)}{7}=4$$   reorder the following

• Divide both sides by -3

• Subtract 12 from both sides

• Multiply both sides by 7

1

2

3

• 1
• 2
• 3

Multiple Choice

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
3x - 8 = 3(x - 4) + 1

• one
• no solutions
• infinite solutions

Multiple Choice

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
3x - 7 = 3(x - 3) + 2

• one
• no solutions
• infinite solutions

Multiple Choice

Identify the number of solutions the equation has. 
4x + 5 = 2(2x +3)

• one solution
• no solution
• infinitely many solutions
• two solutions

Multiple Choice

Determine the type of solution you will have if you get
4=4

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

-4(3x + 2) = 3(-4x + 5)

• No Solution

• One Solution

• Infinite Solution

Multiple Choice

-5(2x - 4) = 2(10 - 5x)

• No Solution

• One Solution

• Infinite Solution

Multiple Choice

What is the LCM of 2, 4, and 6?

• 8

• 12

• 16

• 24

Multiple Choice

What is the LCM of 2, 4, and 9?

• 18
• 36
• 27
• 40

Multiple Choice

What is the LCM of 4 and 10?

• 4

• 20

• 30

• 40

Multiple Choice

What is the LCM of 6 and 9?

• 12

• 18

• 24

• 30

Fill in the Blank

Solve: $$\frac{x+2}{4}=-2$$  

Fill in the Blank

Solve: $$\frac{5-y}{3}=2$$  

Multiple Choice

Find the value of 'x'

$$\frac{3x-2}{3}=\frac{x-1}{3}$$  

• $$\frac{1}{3}$$  

• 2

• $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

Multiple Choice

Find the value of 'x'

$$\frac{3x}{2}+\frac{x-2}{3}=3$$  

• 3

• 4

• 2

• $$\frac{3}{2}$$  

Multiple Choice

Find the value of 'a'

$$\frac{3}{1-a}-\frac{2}{a-1}=0$$  

• -4

• 5

• 4

• 3

Multiple Choice

Find the value of 'a'

$$\frac{a}{3}+\frac{a-3}{6}=\left(a-2\right)$$  

• 3

• 4

• 5

• 6

Multiple Choice

Find the value of 'x'

$$\frac{x+3}{6}+\frac{x}{2}=\frac{3-x}{3}$$  

• $$\frac{1}{2}$$  

• 2

• $$\frac{1}{3}$$  

• 3