How Many Solutions?

​Solving Linear Equations

​(How Many Solutions?)

​

​

​September 20th, 2021

​Constants and Variable Terms

​Constant - a constant is a number on its own

​​Example: in

"x + 5 = 9"

5 and 9 are constants.

​

​Variable Term - a number and a variable side by side

​Example in

​4x + 7 = 5x - 35

​4x and 5x are variable terms

Multiple Choice

A number on its own that does not change and is without a variable is known as a _______________.

• Term

• Variable

• Coefficient

• Constant

Multiple Choice

10 is the ______ in the expression 10 + 2y

• constant

• coefficient

• variable

• like term

Multiple Choice

Identify the constants in the expression:

7-5x+1

• 7

• 1

• 7 & 1

• 5

Coefficient

​The number in front of the variable is called the coefficient

​

​For example:

​In 4x the coefficient is 4

​in -6x the coefficient is -6

Multiple Choice

4 is the __________ of 4n.

• equation

• variable

• coefficient

• solution

Multiple Choice

Identify the coefficients in this expression. 3x + 5x = 4

• 3x, 5x

• 4, 3x, 5x

• 3, 5

• x

​Like Terms

​- Are terms that have the same variables and powers. The coefficients do not need to match.

​

​-7x and 2x are like terms because they are both "x".

​

-3x² and −2x² are like terms because they are both "x²".

​

But 7x and 7x² are NOT like terms (the exponents are different), they are unlike terms.

​

Multiple Choice

True or False: 4x and x are like terms.

• True 

• False

Multiple Choice

What are the like terms in the following expression?

5x + 8 + 2x

• 5x, -2x

• 5x, 2x

• 5x, 8

• 8, -2x

​Rules to Solving Linear Equations

​1. Remove any Parenthesis by doing the distributive property.

​

​2. Put boxes around variable terms and circles around constants.

​

​3. Combine all like terms (circles with circles, boxes with boxes), left side first then right side.

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​4. Determine how many solutions the equation have by comparing like terms and constants to each other on the left and right side of the equal sign.

Multiple Choice

How many solutions?

3x + 8 = 9 + 3x

• One solution

• No solutions

• Infinitely many solutions

Multiple Choice

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

Multiple Choice

$$2x+1=x+8$$  

• one solution

• no solution

• infinite solutions

Multiple Choice

$$4-2x=2x-4$$  

• one solution

• no solution

• infinite solutions