Unit 2 Review

Unit 2 Review

Solving Equations:

• Main goal is to get the variable by itself (isolated)

• The variable is a letter that represents an unknown number (mystery)

• Combine like terms is when we bring together the matching variables.

• Distributive property is when we multiply with (). ex 3(x + 2)

• Remember to always use the sign infront of the number.

Inverse opertaions:

Remember what we do on one side we must do to the other side.

Multiple Choice

What does 3x mean?

• A. Three times X
• B. Three divided by X
• C. Three and X

Multiple Choice

Using the "opposite operation" to "undo" and isolate the variable when solving an equation is more commonly called...

• Inverse operations
• math
• variable
• PEMDAS

Multiple Choice

What is the next step to solve this equation?
3x - 5 = 7

• Add 5 to both sides of the equation

• Add 3x to both sides of the equation

• Subtract 5 from both sides of the equation

• Subtract 7 from both sides of the equation

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

What is the first step to solve this equation?
k + 6 = -4k - 9 

• Add k to both sides of the equation

• Add 4k to both sides of the equation

• Subtract 9 from both sides of the equation

• Subtract 4k from both sides of the equation

Multiple Choice

What is the first step to solve this equation?
3x + 6 = 10 + 3x + 4x 

• Add 4x to both sides of the equation

• Combine like terms 3x and 4x on the same side of the equation

• Add 3x and 6 to get 9x

• Add 6 and 10 to get 16

Multiple Choice

Which step cannot be performed first when solving the equation
5 - 2(x - 7) = x + 1 + 3x

• Distributing -2 to (x - 7)
• Combining x and 3x
• Subtracting 1 from both sides
• 5 - 2

Multiple Choice

2x + 3(5x - 7) = 47

• x = 1
• x = 2
• x = 3
• x = 4

Multiple Choice

Solve the equation:

^x/₃+ 10 = 15

• x = 75

• x = 15

• x = 25

• x = 5

Multiple Choice

Solve for v.

• v = 60

• v = -3

• v = 15

• v = 3

Multiple Choice

8v - 4(v + 8) = 8

• v = 2

• v = 10

• v = 4

• v = -4

Multiple Choice

Solve the equation:

½ (2x + 6) = 3x + 13

• No solution

• x = 8

• x = -5

• x = 7

Multiple Choice

Solve:

2(2x + 3) = -6(x + 9)

• x = 1.2

• x = 6

• x = -6

• x = 7.5

Multiple Choice

3x - x + 4 = 4(2x +1)

• no solution

• all real numbers (infinite)

• x = 6

• x = 0

Inequalities

• Same process as solving equations

• Remember to reverse the inequality when you multiply or divide both sides by a negative.

• Reverse the inequality if you reverse sides. Example 7 > 5, if I decide to write the 5 first I need to reverse the inequality as well 5 < 7 or else it will be false 5 > 7

Graphing Inequalities

Multiple Choice

You flip an inequality symbol when you...

• subtract

• multiply and divide only

• multiple by a negative number

• multiple or divide by a negative number

Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥

• <, >

Multiple Choice

Does the given value make the inequality true? x + 9 > 21, when x = 15

• True

• Not True

Multiple Choice

Match the graph with its inequality.

• b > –2

• b < –2

• b ≥ –2

• b ≤ –2

Multiple Choice

Which number line best represents the solution to the inequality 5w < 30

• A

• B

• C

• D

Multiple Choice

What inequality does the number line graph represent?

• x > 5

• x < −5

• x ≥ 5

• x ≥ −5

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

4x + 1 > 13

• x > 48

• x < 3

• x > 3.5

• x > 3

Multiple Choice

-9x + 7 ≥ 25

• x ≥ -3.6

• x ≤ 2

• x ≥ -2

• x ≤ -2

Multiple Choice

-1(2x + 4) ≥ 6

• x ≤ -5
• x ≥ -5
• x ≤ -1
• x ≥ -1

Word Problems

Look up translation words for help

Consecutive Problems

Consecutive: x , x + 1 , x + 2 .....

Cons. EVEN or ODD: x , x + 2 , x + 4 .

Multiple Choice

Pristine House Cleaners charges $19.85 plus $32 a room. Sparkle House Cleaners charges $61.85 plus $18 a room. Write and solve an equation to find the number of rooms for which the total cost of both house cleaners is the same.

• 4 Houses

• 1/3 Houses

• 3.5 Houses

• 3 Houses

Multiple Choice

Three less than one-half a number is -71.

• $-\frac{1}{2}n+2=-71$

• $\frac{1}{2}n-3=-71$

• $2n-\frac{1}{2}=-71$

• $3-\frac{1}{2}n=-71$

Multiple Choice

Mrs. Burrell is buying donuts for a morning study session. She can spent $35. If it costs $3 per donut and $2 for a chocolate milk for herself, how many donuts did she buy for her students?

• 12 donuts

• 14 donuts

• 10 donuts

• 11 donuts

Multiple Choice

The sum of five times a number and -6 is -2.

• $-6n+5=-2$

• $5n-(-6)=-2$

• $5n+(-6)=-2$

• $\frac{n}{5}-6=-2$

Multiple Choice

Marianna wants to buy a new tennis racket that costs $57.50. She has $8 and plans to save $4.50 each week. How many weeks will it take her to save the money?

•  $10\ weeks$  

•  $11\ weeks$  

•  $15\ weeks$  

•  $24\ weeks$  

Multiple Choice

An electrician charges $42 per hour. He estimates that he will need $628 in materials for a project and the total cost of the project will be $1,384. How many hours does the electrician expect the job to take?

• 18 Hours

• 33 Hours

• 42 Hours

• 48 Hours

Multiple Choice

It costs Doug $30 to set up a cupcake stand. He charges $2 for every cupcake he sells. If Doug makes $48 of profit in one day, how many cupcakes does he sell?

• 14 cupcakes

• 24 cupcakes

• 12 cupcakes

• 39 cupcakes

Multiple Choice

Justin is purchasing a new iPhone.  The sales clerk says that if he pays $100 now his monthly payments will be $25 and his total cost will be $600.  Which equation can be used to determine how many months Justin will be paying for his phone? 

• 25x + 100 = 600
• 25x - 100 = 600 
• 600 - 100x = 25
• 600 + 25x = 100 

Multiple Choice

A gymnastics center charges a $60 registration fee and $15 per class. Olivia registers to take a class and pays a total of $210. Which equation can be used to determine how many classes Olivia signed up for?  

• 60 - 15x = 210 
• 15x - 60 = 210
• 15x + 60 = 210 
• 210 + 15x = 60 

Multiple Choice

The sum of two consecutive integers is 123. What is the smallest of the two integers?

• 60

• 61

• 62

• 63

Multiple Choice

Find three consecutive odd integers whose sum is -45.

• -15, -17, -19

• -17, -18, -19

• -13, -15, -17

Multiple Choice

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she can spend no more than $35 in all.

• .50x + 20 ≥ 35

• .50x < 35

• .50 + 20x ≤ 35

• .50x - 20 = 35

Multiple Choice

A limo driver needs to make more than $450 in one day.  He charges a rental fee of $375 and $0.85 per mile.  What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450
• 0.85x + 375 < 450
• 0.85 + 375x > 450
• 0.85 + 375x < 450

Special Cases:

Infinite Solutions and No Solution

• Remember all variables need to cancel out.

• If what remains is true 7 = 7, then infinite solutions

• If what remains is false 5 = -5, then no solutions

Multiple Choice

Identify if this equation has one solution, infinitely many solutions or no solution.

-3x+1=x+9-4x

• One solution

• Infinitely many

• No solution

Multiple Choice

4(-8x + 5) = -32x - 26

• x = 54

• x = -54

• Infinite solutions

• No solution

Multiple Choice

2x + 1 = 2(x -10)

• No Solution

• x = 0

• all real numbers (infinite)

Multiple Choice

3x - 7 = 3(x - 3) + 2

• one
• no solutions
• infinite solutions

Multiple Choice

3x + 15 = 3(x + 5)

• No Solution
• x = 15
• all real numbers (infinite)

Multiple Choice

Describe the solution set:
2(x + 5) = 2x + 5

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

Solving Literal Equations

Equations with more than one variable

Multiple Choice

Solve for t.

D= rt

• $t=\frac{D}{r}$

  
  

• $t=Dr$

• $r=\frac{D}{t}$

• $r=Dt$

Multiple Choice

pV = nRT

solve for R

• $R=\ \frac{pV}{nT}$

• 
  

  $R=\frac{p}{n}+\frac{V}{T}$

• $R=pV-nT$

• $R=\frac{pV\ -\ n}{T}$

Multiple Choice

Solve:
12x - 4y = 20  ,  for   y 

• y = 3x - 5
• y = -3x + 5
• y = -3x - 5
• y = 3x + 5

Multiple Choice

8x + 4y= 16

• y = -8x + 16
• y = 2x -4
• y = -2x + 4
• y = -8x + 12