C14. (Intro) Further Solving of Equations and Inequalities

"Algebra is like a puzzle. The numbers are the clues, and solving it is the game."

Today's Quote

Fill in the Blanks

I’m a number. Multiply me by 2, then add 6. You get 18. What number am I?

Fill in the Blanks

I’m a number. Double me, then subtract 4. The result is 10.

What number am I?

Fill in the Blanks

In 5 years, I’ll be 3 times as old as I was 5 years ago. How old am I now?

Multiple Choice

Which of the following expressions has a variable?

• $$x+19$$  

• $$2^2$$  

• $$6+9$$  

• $$2\left(1-4\right)$$  

Math Response

In 5 years, I’ll be 3 times as old as I was 5 years ago. How old am I now?

Type answer here

Correct Answer: 10

Deg^°

Rad

Introduction to Algebra

By: Fatmawati, S.Si., M.Ed., Gr.

​Cambridge IGCSE 0580

What is algebra?

Algebra is a branch of mathematics that uses symbols (usually letters) to represent numbers in formulas and equations.

Cambridge IGCSE 0580

Algebra is a language.

• In many ways, learning algebra is much like learning any other language.

• Just like sentences use words to describe thoughts, algebra uses expressions to describe patterns and relationships.

Cambridge IGCSE 0580

• In algebra, a letter is often used to stand for a number.

• The letter used ​to stand for a number is called a variable.

  • Some common letters used as variables​ are x, y, z, a, b, c, and n. ​

• When a letter is used to stand for a number, the number is unknown. Think of those letters as "mystery numbers."

Multiple Choice

Which of the following expressions has a variable?

• $$16-5$$  

• $$14+3n$$  

• $$2\cdot4\left(1+3\right)$$  

Multiple Choice

What is the variable in the following expression?

$$2\left(y+7\right)$$  

• $$7$$  

• $$2$$  

• $$y$$  

Multiple Choice

What is the variable in the following expression?

$$23+2x$$  

• 23

• 2

• $$2x$$  

• $$x$$  

• ​A variable can be a part of an expression, an equation, or an inequality.

• An expression is part of a mathematical sentence, just as a phrase is ​part of an English sentence.

  • 2n + 4 ; 3y ; 6 + x

• A mathematical sentence ​contains two expressions joined by an equal sign or an inequality sign.

  • 2h + 4 ≥ 13​ ; p + 4 = 9

• An equation is a mathematical sentence in which two expressions are joined by an equal sign. ​

  • ​c - 8 = 1 ; 4t + 9 = 17

Cambridge IGCSE 0580

Match

Match the following

• A letter or symbol that represents an unknown number or value (e.g., x in 3x + 5).

• A number that multiplies a variable (e.g., 3 is the coefficient in 3x).

• A fixed number that does not change or contain a variable (e.g., 5 in 3x + 5).

• A group of numbers, variables, and operations without an equal sign (e.g., 3x + 5).

• A mathematical statement showing that two expressions are equal, with an equal sign (e.g., 3x + 5 = 20).

Variable

Coefficient

Constant

Expression

Equation

• Variable

• Coefficient

• Constant

• Expression

• Equation

Multiple Select

Select all the expressions.

• $$9x<18$$  

• $$2d$$  

• $$c=3$$  

• $$4t-4$$  

Multiple Select

Select all the expressions.

• $$3x-8$$  

• $$4c$$  

• $$2x>6$$  

• $$8+y$$  

• ​An inequality is a mathematical statement in which two phrases are joined by an inequality symbol.

  • < "less than"

  • > "greater than"

  • ≤ "less than or equal to"

  • ​≥ "greater than or equal to"

  • ​Examples:

    • 3a < 9 ; f ≥ 4

Intro to Algebra | Robinson

Multiple Select

Select all the expressions.

• $$a-4$$  

• $$5y$$  

• $$4d+6=26$$  

• $$18<p+9$$  

Multiple Choice

Is the following an expression or an equation?

$$2x-4$$  

• an expression

• an equation

Multiple Choice

Is the following an expression or an equation?

$$5f+20=30$$  

• an expression

• an equation

Multiple Choice

Is the following an expression or an equation?

$$x=14$$  

• an expression

• an equation

Multiple Choice

Is the following an equation or an inequality?

$$4t<92$$  

• equation

• inequality

• neither

Multiple Choice

Is the following an equation or an inequality?

$$x=5$$  

• equation

• inequality

• neither

Multiple Choice

Is the following an equation or an inequality?

$$7+y\le9$$  

• equation

• inequality

• neither

Multiple Choice

Is the following an equation or an inequality?

$$5z$$  

• equation

• inequality

• neither

Multiple Choice

Which symbol means "greater than"?

• $$<$$  

• $$=$$  

• $$>$$  

• $$\ge$$  

Multiple Choice

Which symbol means "less than or equal to"?

• $$<$$  

• $$=$$  

• $$\ge$$  

• $$\le$$  

Multiple Choice

What does this mean?

$$\ge$$  

• greater than

• greater than or equal to

• less than

• less than or equal to

Multiple Choice

What does this mean?

$$<$$  

• greater than

• less than

• greater than or equal to

• less than or equal to

Multiple Choice

What are variables in math?

• Letters

• Numbers

• Expressions

Multiple Choice

A variable represents what is ______________. 

• the answer
• the operation
• the difference
• unknown 

Multiple Choice

A variable is . . .

• an awesome number

• a number represented by a letter

• an infinite number

• a number multiplied by another number

Multiple Choice

5p + 4h - 2
Which are the variables? 

• 5p, 4h, 2
• 2
• p, h
• 5, 4

Multiple Choice

What is the variable in 3x - 5

• x

• 5

• 3

Multiple Choice

What is the value of d in the following equation?
15 + d = 27

• 13
• 12
• 14
• 8

Multiple Choice

What is the value of q in the following equation?
6 + q = 4 + 5

• 2
• 5
• 3
• 4

Multiple Choice

a mathematical sentence stating that two expressions are equal

• term

• coefficient

• equation

• variable

Multiple Choice

An equation...

• has an equal sign

• does NOT have an equal sign

Multiple Choice

Bob ran 6 miles yesterday. He wants to run double the amount today. How much will Bob run today?

• 18 miles

• 12 miles

• 24 miles

• 30 miles

Multiple Choice

Frank made 20 cookies. He gave 5 of them to his mom. How many cookies does Frank have left?

• 5 cookies

• 20 cookies

• 15 cookies

• 0 cookies

Multiple Choice

Charlotte made 40 cookies. She wants to give an equal amount to 4 of her friends. How many cookies should she give each friend?

• 4 cookies

• 5 cookies

• 8 cookies

• 10 cookies

Untitled Lesson

By Fatmawati Fatmawati