Solving Algebraic Equations

Mixed equations

100

2z - 31= -9z + 24

Solve for z

z = 5

200

3-10b = 2b-9

b = 1

300

Translate the following: 

A number divided by 8, minus 6, is 15.

(don't solve)

x/8 - 6 = 15

400

Translate the following

Five less than three times a number is 12

do not solve

3x - 5 = 12

500

Hans needs to rent a moving truck. Suppose Company A charges a rate of $40 per day and a $60 fee and Company B charges a $80 fee plus $20 a day. For what number of days is the cost the same?

Let x = days

40x + 60 = 20x + 80

The cost is the same the first day

Multi-Step Equations

100

-3m - 1= 8

What is m?

m = -3

200

-c - 2.1 = -14.7

Solve for c

-c - 2.1 = 14.7

     -c = 16.8

       c = -16.8

300

-3a + 11 -7a = -9

What is the value of a?

a = 2

400

6(a + 3) = -6

Find the value of a.

a=-4

500

9y - 6 - 6y = 6

What is the value of y?

y = 4

Multi-Step Equations

100

8b + 3b = 22

What is b?

b = 2

200

-14 = 10 + 24x

What is the value of x?

x=-1

300

2a + 5(a - 4) = 8

What is the value of a?

a = 4

400

6(2y + 6) - 4y - 5= 25

What is the value of y?

y= -3/4

500

-6(m + 1) + 18 = 24

What is the value of m?

m = -2

Distribution Multi-Step Equations

100

64 = 8(r + 2)

What is r?

r = 6

200

7(f - 1) = 49

What is f?

f = 8

300

5(d - 2) = 40

What is d?

5(d - 2) = 40

5d -10 = 40

5d = 50

d = 10

400

72 = 5(4x + 10) +2

72 = 5(4x + 10) +2

72 = 5(4x + 10) +2

What is x = 1

500

9(y - 4) - 7y = -18

What is y?

9y - 36 - 7y = -18

2y - 36 = -18

2y = 18

y = 9

Word Problems

100

Julie is 3 years older than her sister. The sum of their ages is 19. How old is Julie's sister? 

Create let statements and solve

Let x = her sisters age

Let x + 3 = Julies age

x+ x + 3 = 19

2x + 3 = 19 

Her sister is 8 years old

200

We are at a Chicago Cubs baseball game. We buy 4 hotdogs and 1 drink. We spend a total of $17. If the drink costs $5, how much does one hotdog cost? AND What equation can you use to solve this? 

4x + 5 = 17 

One hotdog costs $3

300

The sum of three consecutive integers is 84. Find the largest integer

Create let statements and solve

Let x = 1st integer

x + 1 = 2nd integer

x + 2 = 3rd integer

x + x +1 + x + 2 = 84

3x + 3 = 84

x= 27

The largest integer is 29!

400

You have a part time job. You work 9 hours on Saturday. You also receive an allowance of $20 per week. You earn $92 this week. How much do you earn PER HOUR at your part time job? AND What equation can you use to solve this?

9x + 20 = 92

You earn $8 per hour

500

Sandy found a tree by the curb and wants to decorate it. After budgeting a total of $55.00 to decorate the tree, she began by spending $15.00 on tinsel. She spent the rest on five ornaments. What is the cost of each ornament?

Let x = cost of each ornament

5x + 15 = 55 

Each ornament costs $8