Multistep Equations and Multistep Inequalities

Solve Multistep Equations

100

- 5(x- 2) - (x + 2) =50

What is  x = -7

200

8 - 3(k + 2) = 2 - 3k

What is 2 = 2 

Infinite Solutions

300

3w - (7w + 12) = 2(w - 3)

What is w = - 1

400

8=8v-4(v+8)

What is v=10

500

5(2x+6)=-4(-5-2x)+3x

What is x=10

Solve proportion & graphing multistep inequalities

100

4     =    12

5            2y - 3

What is y = 9

60 = 4(2y - 3)

60 = 8y - 12,   72 = 8y,     9 = y

200

  5     =    3   

y - 7       y - 5

5(y - 5) = 3(y - 7)

5y - 25 = 3y - 21

2y - 25 = -21

2y = 4

y = 2

300

-2(x+3)<10

Show graph for: x>-8

400

2(x + 1) < -3x - 13

2x + 2 < -3x - 13

5x + 2  <  - 13

5x < -15

 Show graph for: x < -3

500

9n - 6 < 5n + 18

Show graph for: n<6

Absolute Value & Literal Equations

100

|x +1| = 6

x + 1 = 6 and x + 1 = -6

x = {-7, 5}

200

Solve the Absolute Value Equations.

|6c - 18| = 30

6c -18 = 30 and 6c - 18 = -30

c = 8   and c = -2

c = {-2, 8}

300

Solve multistep absolute value.

|2x - 1| = 17

x = {-8, 9}

2x -1 = 17, 2x -1 = -17

2x = 18, 2x = -16

x = 9, x = -8,

400

Solve Multistep Absolute Value

|3 - 6p|    =        -9

 -5           

p = {-7, 8}

 (-5)|3 - 6p| / -5  = -9 (-5)

   |3 - 6p| = 45                  |3 - 6p| = -45

3 - 6p (-3) = 45 -3             3 - 6p (-3) = -45 -3

-6p = 42, p = -7                -6p = -48, p = 8

500

Solve V = 1/3*pi *r^2*h for h

3V/pi*r² = h

Multistep equations and compound inequalities

100

6a+5a=-11

What is a=-1

200

Solve w = 9x + 5y   for y

What is 

w - 9x   = y

    5

300

Solve the inequality, graph, and write using Interval notation

5(x + 8) -7 < 23

5x + 40 -7 < 23

5x + 33 < 23

5x < -10

graph x < -2

Interval Notation (-oo, -2]

400

Solve the compound inequality, graph, and write using Interval notation

-2x - 1 < -17 or 1 - x > 4

-2x < -16     or    -x > 3

   x > 8         or     x < -3

graph:  x > 8         or     x < -3

Interval Notation: (-oo, -3] or (8, oo)

500

Solve, Graph & Write using Interval Notation

-24 < 2x - 10 < -6

What is -7 < x < 2

Graph: -7 < x < 2

Interval Notation [-7, 2)

Word Problems

100

The larger of two numbers is two more than five times the smaller number.  If the sum of the two numbers is 80, find both numbers

What is 13, 67?

Let x = smaller number, Let 5x + 2 = 80

x + 5x + 2 = 80

6x = 78

x = 13, 5(13) + 2 = 67

200

The larger of two numbers is nine less than four times the smaller number. If the sum of the two numbers is 76, find both numbers.

What is 17 and 59

Let x = smaller

Let 4x -9 = larger

x + 4x - 9 = 76

5x =85, x = 17, 4(17) - 9 = 59

300

The length of a rectangle is two more than three times its width. If the perimeter of the rectangle is 92 meters, find the dimensions. 

NOTE use: P = 2L + 2w

Let x = width, let 3x + 2 = length

2(x) + 2(3x+ 2) = 92

2x + 6x + 4 = 92

8x = 88

x = 11

What is 11 meters, 35 meters

400

As part of their togovernment class, Maddie and Ryan had to log volunteer hours in their community. Ryan volunteered for one more than three times the number of hours that Maddie did. Altogether, they volunteered in their community for 45 hours, how many hours did Ryan Volunteer?

Let x = Maddie's hours

Let 3x + 1 = Ryan's hours

 x + 3x + 1 = 45

4x = 44, x = 11

Ryan worked 3(11) + 1 =34 hours

500

Maria and Tim sold candy bars for a fundraiser. Maria sold seven less than twice the number of candy bars that Tim sold. In total Tim sold 137 candy bars.  How many candy bars did Maria sell?

What is ... 89 Candy Bars.

Let x = Tim's sales, let 2x - 7 = Maria's sales

x + 2x - 7 = 137

3x = 144,  x = 48, 2(48) -7 = 89