Do all equations only have one solution?

In this lesson you will learn that a linear equation has

infinitely many solutions by transforming it into a simpler

form.

Let’s ReviewLet’s Review

X + 2 = 5

Let’s ReviewLet’s Review

X + 2 = 5

-2 -2

X = 3

Let’s ReviewLet’s Review

X = 3

Let’s ReviewLet’s Review

X + 2 = 5

Let’s ReviewLet’s Review

X+ 2 = 5 X+ 2 = 5

5 = 5

3 + 2 = 5 4 + 2 = 5

6 = 5

Let’s ReviewLet’s Review

X + 2= 5

Let’s ReviewA Common Mistake

Assuming all linear equations have only one solution

Let’s ReviewA Common Mistake

X+ 2 = 2 + X X+ 2 = 2 + X

3 = 3

1 + 2 = 2 + 1 0 + 2 = 2 + 0

2 = 2

Let’s ReviewCore Lesson

What is the solution for x – 3 = x + -3?

x – 3 = x + -3

X = X

+ 3 = +3

x – 3 = x + -3

5 -3 = 5 + -3

2 = 2

Infinitely Many Solutions

Let’s ReviewCore Lesson

What is the solution for x – 3 = x + -3?

x – 3 = x + -3 -x = -x

-3 = -3

x – 3 = x + -3

-2 -3 = -3 + -2

-5 = -5

Infinitely Many Solutions

Let’s ReviewCore Lesson

How many solutions does 5(x+1) = 5x+5 have?

5(x+1)= 5x+5

-5 = -5

5x+5 = 5x+5

5x = 5x5 = 5x = x

Infinitely Many Solutions

Let’s ReviewCore Lesson

How many solutions does 5(x+1) = 5x+5 have?

5(x+1)= 5x+5

-5x =-5x

5x+5 = 5x+5

5 = 5Infinitely Many

Solutions

In this lesson you learned that a linear equation has infinitely

many solutions by transforming it into a simpler

form.

Let’s ReviewGuided Practice

How many solutions does 4x = 4x have?

Let’s ReviewGuided Practice

What is the solution for x + x = 2x?

Let’s ReviewExtension Activities

When we solve the equation 2(x+1) = 2x+2, what is our solution? What does this mean?

Let’s ReviewExtension Activities

How many solutions does the equation y=y have? Why?

Let’s ReviewExtension Activities

Create an equation that has only one solution and that has infinitely many solutions.

Let’s ReviewQuick Quiz

How many solutions does x+1=1+x have?a) One b) Many

How many solutions does 4(x+1) = 4x+4 have?a) One b) Many