Math 7: Unit 3

One-Step Equations

100

Solve for x:

x + 12 = 20

x = 8

200

Solve for x:

-10x = 80

x = -8

300

Solve for x:

(x ÷ 4) = 11

(hint: write x/4 as a fraction on whiteboard)

x = 44

400

Translate (write equation) & solve:

The difference between a number and nine is 14

n - 9 = 14

n = 23

500

Translate (write equation) & solve:

Half of a number is equal to 13

(1/2)n = 13

n = 26

Two-Step Equations

100

Solve for x:

2x + 4 = 20

x = 8

200

Solve for x:

-9 + (x/6) = -10

x = -6

300

Solve for x:

2 = (x + 5)/6

(write out on whiteboard to see fraction normally)

x = 7

400

Translate (write equation) & solve:

Eight less than ten times a number is 122

10n - 8 = 122

n = 13

500

Translate (write equation) & solve:

The sum of negative nine and a number, divided by four, is negative 6

(-9 + n)/4 = -6

n = -15

Word Problems: 1 & 2 Step Equations

100

A rectangular rug as an area of 38.5 square feet.  If the rug is 5 feet wide, what is the length of the rug?

(hint: what's the formula for area of rectangle?)

Define your variable!

Label

Let l = length

5l = 38.5

l = 7.7 ft

200

Daniel bought movie tickets for 6 friends.  If he paid a total of $67.50 for the tickets, what was the cost of one movie ticket?

*Define your variable!

Label

Let t = ticket cost

6t = 67.5

t = $11.25

300

Lane is fourteen years older than Michelle.  If Lane is 33, how old is Michelle?

Define your variable!

Label

Let M = Michelle

14 + M = 33

M = 19 years old

400

Setup equation & solve:

Madison has a beach chair and umbrella stand.  Each umbrella rents for $19 per day.  At the end of one day, she made $130 off beach chair rentals and the rest from umbrella rentals.  If she made a total of $567, how many umbrellas did she rent that day?

Define variable & label!

Let u = umbrella

19u + 130 = 567

u = 23 umbrellas

500

Setup equation & solve:

Victoria spend one-fourth of her birthday money on clothes.  She received another $25 a week later.  If she has a total of $70 now, how much did she have before she went shopping?

Define variable & label!

Let m = money before shopping

(3/4)m + 25 = 70

m = $60

Multi-Step Equations

100

Solve for x:

2(x + 1) - 7 = 5

2x + 2 - 7 = 5

2x - 5 = 5

2x = 10

x = 5

200

Solve for x:

5(6x + 5) = -25 + 5x

30x + 25 = -25 + 5x

25x = -50

x = -2

300

Solve for x:

-8(-5x + 7) = 7(7x + 1)

40x - 56 = 49x + 7

-63 = 9x

-7 = x

400

Translate (write equation) & solve:

The sum of 4 and a number, divided by two is less than 6

(4 + n)/2 < 6

n < 8

500

Setup equation & solve:

Nancy has $240 in the bank.  She wants to buy as many $15 video games as possible.  How many could she buy if she wanted to keep at least $120 in the bank?

Define variable & label!

Let v = video game

240 - 15v ≥ 120

v ≤ 8 video games

Inequalities

100

solve AND graph the following:

x + 1 ≤ -8

x ≤ -9

teacher check

200

BONUS:

first group to draw a Christmas tree with 3 ornaments wins the points

teacher selects

300

solve AND graph the following:

-3x + 5 > 23

x < -6 *needed to FLIP 

check graph

400

The difference of a number and 5 is a maximum of 14

WRITE and SOLVE the inequality

x - 5 ≤ 14

x ≤ 19

500

Marvin can fit no more than 18.5 gallons in his gas tank.  If he stops at the gas station and has 3.7 gallons left in his tank, how much gas can he add to his tank?

WRITE the inequality and SOLVE

3.7 + x ≤ 18.5

x ≤ 14.8