Determine number of solutions Review

Solving Equations with Variables on Both Sides - Determining the Number of Solutions:
- One Solution
- No Solution
- Infinitely Many Solutions

​A whole class mixed review supplement for Lessons 3.4 a & b

You need access to pencil, paper, and your hand-held calculator! The following questions are timed and graded!!

Multiple Choice

7x = 3x + 24

• 6

• 10

• 14

• 4

You need access to pencil, paper, and your hand-held calculator! The following questions are timed and graded!!

Multiple Choice

Solve the equation
12x - 15 = 3(2x+3)

• x = 4
• x = -4
• x = 2
• x = -2

Multiple Choice

Solve:

5y+34 = -2(-7y+1)

• y = -4

• y = 9

• y = 4

• y = 36/19

When Solving Equations with Variables on Both Sides, if you can isolate the variable, your answer will be ONE SOLUTION!

Vocabulary

Identity - An equation that is true for every possible value of the
variable. After simplifying, both sides of the equation are identical (same coefficients, variables, & constants on each side).

• This means you can replace the variable with any value to make the
equation true and the expressions on each side are equivalent.

Example: x+1=x+1

When determining the number of solutions, this is often referred to as INFINITELY MANY SOLUTIONS or ALL REAL NUMBERS

Vocabulary

If after simplifying both sides of the equation, you end up with the same coefficients & variables on each side; but different constants, then the variables will cancel out.
• These equations have no solution and there is no value of the variable that makes the equation true.

Example: x+1=x+2


When determining the number of solutions, this is referred to as NO SOLUTION or Empty Set ∅ = { }.

Learning Objective-

I can distribute & combine like terms to simplify each side of the equation and then apply inverse operations in order to solve equations with variables on both sides. I can compare coefficients, variables, & constants of simplified equations in order to identify whether equations have One Solution, No Solution, or are identities (All Real/IMS)

Fill in the Blank

$$-3.6a+1=-3.6\left(a-1\right)$$ Does the equation have an identity or no solution? 

Multiple Choice

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides
• Subtract 11 from both sides
• Add 11 to both sides
• Divide 3 on both sides.

Multiple Choice

Solve the equation:
7x - 4 = 3 + 8x

• x = 7
• x = -7
• x = 2/7
• x = 11

Multiple Choice

When you solve an equation you get 8=8. How many solutions does that equation have?

• One

• None

• Infinite

Multiple Choice

When you solve an equation you get x=4. How many solutions does that equation have?

• One

• None

• Infinite

Multiple Choice

When you solve an equation you get 5=3. How many solutions does that equation have?

• One

• None

• Infinite

Multiple Choice

How many solutions? 10+3x=5(x-2)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

How many solutions? -x-(-10)= -(x-10)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

How many solutions? -3x-5+5x=2(x+7)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

How many solutions? 3x+2=2+3x

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

How many solutions? 2(x+3)=2x+6

• One Solution

• No Solution

• Infinitely Many

Word Cloud

In 1 word, describe how you are feeling today...