Algebra Unit 2

Solving Equations

100

Solve.

4x – 6 = 14

x = 5

200

Solve.

5(x + 1) = –35

x = –8

300

Solve.

5n + 5 = 3n + 21

n = 8

400

Solve.

0.5(6b + 4) = 0.25(8b + 24)

b = 4

500

Solve.

3d – 2 = –d + 16.25
   8                      

d = 12

How Many Solutions?

100

How many solutions?

–6y + 3 = 3 – 6y

3 = 3

Infinite

200

How many solutions?

8q + 10 = 4(3 + 2q)

10 = 12

None

300

How many solutions?

8(z + 6) = 4(2z + 12)

48 = 48

Infinite

400

How many solutions?

 1 ( 1 m – 8) =  1 (m – 16)
 2   2                 4       

–4 = –4

Infinite

500

Identify the mistake that was made. Then determine the correct answer.

3b – 13 + 4b = 7b + 1
        7b – 13 = 7b + 1
      14b – 13 = 1
             14b = 14
                 b = 1
            One solution

Mistake: Adding 7b + 7b

Answer: –13 = 1, No solution

Absolute Value

100

Solve.

|–2y + 6| = 6

y = 0, y = –6

200

Solve.

|4x – 2| = 26

y = 7, y = –6

300

Write an absolute value equation with solutions x = 8 and x = 22.

|x – 15| = 7

400

|8k – 5| = –4

No solution

500

Solve.

4 – 3|q| = 10

No solution

Proportions

100

Solve.

 3  = 15
 8      a

a = 40

200

Solve.

 15  =  g 
 35      7

g = 3

300

Solve.

 6  =    15   
14      x – 3

x = 38

400

Solve.

 m + 1  =  m – 3 
    9             21

m = –4

500

Solve.

    4     =     12    
n + 8       n + 30

n = 3

Rearranging Formulas

100

Solve in terms of t.

d =  t 
       v

t = dv

200

Solve in terms of m.

2p + m = 11

m = 11 – 2p

300

Solve in terms of r.

 v + r  = t
   2

r = 2t – v

400

Solve in terms of g.

g² + 2h = 15k

g = √15k – 2h

500

Jayden is buying video games and controllers. The total amount he is spending is represented by T = 13.50g + c, where g is the number of games and c is the number of controllers.

a. Solve the equation for g.

b. If the controllers cost $55 and he spent $136 total, how many games did Jayden buy?

a. g =  T – c 
          13.50

b. 6 games