2 ENR: Chapter 1 Summative Review

2 ENR: Chapter 1 Summative Review

This summative will start at section 1-3, Solving Equations

• Solving Multi-Step Equations (with distribution)

• Solving Equations with Variables on both sides

• Word Problems (define a variable, write an equation and solve)

• Literal equations

• Let's review!

Multiple Choice

27 = 5r + 2

• 5
• - 5
• 5.8
• - 5.8

Fill in the Blanks

 $\frac{\left(x+2\right)}{3}=7$  

Fill in the Blanks

 $\frac{3x}{4}-6=-18$  

Multiple Choice

Solve for b:

-11 + 3(b + 5) = 7

• b = 1

• b = -1

• b = 3

• b = -3

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3

Multiple Choice

Solve the equation:
4 - 6x - 2= -2(3x-1)

• no solution
• infinitely many solutions
• x = ⅓
• x = 4

Multiple Choice

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

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

Multiple Choice

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

• x = 4
• x = -4
• x = 2
• x = -2

Multiple Choice

Cadin rents a bouncy house for a birthday party.  It costs $30.00 plus $4.00 per hour.  If he spends a total of $78.00, how many hours did he keep the bouncy house?

• $30.00 - $78.00 = $4.00h
• $78.00 + $30.00 = $4.00h
• $30.00 + $4.00h = $78.00
• $30.00 - $4.00h = $78.00

Multiple Choice

Jazmine joined a music club.  The start up fee was $10.00.  Each song she downloads is $0.99.  If she spent a total of $15.94, how many songs did she download?

• $10.00 + $0.99m = $15.94
• $10.00m + $0.99 = $15.94
• $10.00/$0.99m = $15.94
• $10.00 - $0.99m = $15.94

Multiple Choice

Hailey bought a book for $2.50 and 4 stickers.  She spent a total of 6.59.  How much did the stickers cost?

• $2.50 + 4s =$6.59
• $2.50s + 4 = $6.59
• $2.50 - 4s = $6.59
• 4s - $2.50 = $6.59

Multiple Choice

 $3y\ =\ 2g\left(x+h\right)\ \ solve\ for\ x$  

•  $x\ =\ \frac{3y+h}{2g}$  

•  $x\ =\ \frac{3y-h}{2g}$  

•  $x\ =\ \frac{3y}{2g}+h$  

•  $x\ =\ \frac{3y}{2g}-h$  

Multiple Choice

Solve for x:

• x = yb - v
• x = by - v
• x = by + v

Multiple Choice

• b = 3A - a - c
• b = -3A + a - c
• b = -3A - a - c 
• b = 2A - c

Multiple Choice

 $2xy-y=4$  Solve for y.

•  $y=4\left(2x-1\right)$  

•  $y=8x-4y$  

•  $y=\frac{4}{2x-1}$  

•  $y=\frac{3}{2x}$  

Multiple Choice

 $2xy-y=4$  Solve for y.

•  $y=4\left(2x-1\right)$  

•  $y=8x-4y$  

•  $y=\frac{4}{2x-1}$  

•  $y=\frac{3}{2x}$  

Absolute Value Equations

• Absolute value is the distance away from zero on a number line.

• You cannot have an absolute value equation equal to a negative

• Make sure to isolate the absolute value equation on one side first!

• Solve for the positive and negative case

• When the absolute value is equal to 0, there will only be one case

• Word Problems:

   $\left|x-ideal\ \right|=variance$  

Multiple Choice

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4
• x = 5 and x = -5
• Only x = 5
• No Solution

Multiple Choice

Solve for x
l 2x−1 l +4 = 8 

• x = 2.5 and x = -1.5
• x = 2 and x = -1
• x = -2 and x = 9
• No Solution

Multiple Choice

Solve for x

-3 l 4w−1 l −5 = 10

• x = 1.5 and x =-1

• x = -1.5 and x = 1

• x =1 and x = -1

• No Solution

Multiple Choice

Solve for x
3 l 4w−1 l −5 = 10

• x = 1.5 and x =-1
• x = -1.5 and x = 1
• x =1 and x = -1
• No Solution

Multiple Choice

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x - 50|=15

• |x + 15|=50

• |x + 50|=15

• |x - 15|=50

Multiple Choice

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03
• |v-20|=0.03
• |v|-0.03=20
• |v-0.03|=20

Inequalities!

• Follow the same steps as solving an equation except...

• When you multiply or divide BY a negative number, you must flip the inequality sign.

Multiple Choice

m - 5 > 10

• m is less than 15
• m is greater than 5
• m is greater than 15
• m is less than 5 

Multiple Choice

Pick the correct inequality.

• A
• B
• C
• D

Multiple Choice

Solve:
7(x + 3) < 5x + 13

• x>-4
• x < 17
• x<-4
• x > -17

Multiple Choice

At least tells you to use which inequality sign?

•  <
•  >
•  ≤
•  ≥

Multiple Choice

Solve and choose the correct graph:

• A
• B
• C
• D

Multiple Choice

Solve and choose the correct graph:

• A
• B
• C
• D

Multiple Select

Which numbers are possible solutions to the inequality... (SELECT ALL THAT APPLY)

x+6x≤2(2+3x)

• 4

• 100

• 5

• 0

• -100

Multiple Select

Which numbers are possible solutions to the inequality... (SELECT ALL THAT APPLY)

-5x + 10 < 30

• 0

• 100

• -100

• -3

• -4

Compound Inequalities- "and"

• "And" compound inequalities can be written as:

• 
  
   $x<2\ and\ x>-1\$  ;  $-1<x<2$  
  

• These form an intersection on their graphs

Compound Inequalities- "or"

• The "or" compound inequalities will always have the word "or" in it.

• Ex:

   $x\le-2\ or\ x>4$  

• They form a union of the graphs

Multiple Choice

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

Multiple Choice

3x-4< -13 or 7x+1> 22

• All Real numbers

• x>3 and x>-9

• The answer is not listed

• x<-3 or x>3

Multiple Choice

Write an inequality for Graph 3.

• 5 < x ≤ -2

• x ≤ -2 OR x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x < 5

Multiple Choice

Solve and graph:

• A

• B

• C

• D

Multiple Choice

You take a trip to the bowling alley, where each game cost $2, plus you plan to spend $10 on food. You can spend at most $25. Which inequality models this scenario?

• 2x + 10 ≥ 25

• 2x + 10 > 20

• 2x + 10 ≤ 25

• 2x + 10 < 25

Multiple Choice

Every day, a man needs to eat at least 1800 but less than 1900 calories. Write an inequality representing the possible amount of calories you could get.

• 1800 ≤ c ≤ 1900

• 1800 ≤ c < 1900

• 1800 < c ≤ 1900

• 1800 < c < 1900

Absolute Value Inequalities!

• <,  $\le$  will be an "and" graph

• >,  $\ge$   will be an "or" graph

• You cannot have an absolute value less than a negative; this will always be no solution

• You will always have an absolute value greater than a negative; this will be all real numbers

Multiple Choice

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3
• c < -5 1/3  or c > 2 2/3
• c < 5 1/3 or c > -2 2/3
• -5 1/3 < c < 2 2/3

Multiple Choice

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Multiple Choice

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Multiple Choice

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution