Equations and Inequalities

Multi-Step Equations

100

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

x=-7

200

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

w=-1

300

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

Infinite 

400

9(n-4) - 7n = 32 - 2(n+8)

n=13

500

A larger number is five more than twice a smaller number. Their sum is 80. Find the numbers.

25, 55

Proportions

100

2/9 = 4/x+8

x=10

200

6/a-6 = 3/a-3

a=0

300

5/y-7 = 3/y-5

y=2

400

6/2n-5 = 2/n-7

n=16

500

As part of their government 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?

34 hours

Absolute Value Equations

100

lx+1l = 6

{-7,5}

200

l6c-18l = 30

{-2,8}

300

-4l2w+6l = -32

{-7,1}

400

5l4x-4l - 9 = 31

{-1,3}

500

A rectangle has a length six inches less than twice its width. If the perimeter of the rectangle is 54 inches, find the dimensions.

11 in., 16 in.

Literal Equations

100

Solve I=prt; for t

t=I/pr

200

Solve Ax + By = C; for y

y=(C-Ax)/B

300

Solve r=4/3(p-q); for p

p = 3/4r + q

400

Solve m + 2n² = 7m; for n

n = +/- square root of 3m

500

The sum of two consecutive odd numbers is 148. Find the numbers.

73,75

Multi-Step Inequalities

100

Solve, graph, and write in Interval Notation: 

2(x+3) is greater than or equal to 4(x-1)

x is less than or equal to 5; closed circle over 5 and shaded left; (-inf, 5]

200

Solve, graph, and write in Interval Notation:

5x+24 > 2(x-9) - 3x

x>-7, open circle over -7 shaded right, (-7,+inf)

300

Solve, graph, and write in Interval Notation:

-9(x-5) + 9 < 3x + 42

x>1, open circle over 1 shaded right, (1,+inf)

400

Solve, graph, and write in Interval Notation:

2(x+1) is less than or equal to -13 -2x

x is less than or equal to -3, closed circle over -3 shaded left, (-inf, -3)

500

The larger of two numbers is four more than the smaller number. If the sum of the numbers is 74, find the numbers.

35,39