Unit 2 (Chapter 3) Algebra 1 - Solving Equations

Proportions/Percentages

100

x/6 = 10/15

x=4

200

What 32 percent of 80

25.6

300

What percent of 60 is 12

20 percent

400

(x+6)/2=(x+9)/5

x=-4

500

34/6=(2x+1)/3

8

Two-Step Equations

100

Solve for x:

2x + 3 = 15

(When you see it written 2x that means the same thing as 2*x)

x = 6

WORK

2x + 3 = 15

2x + 3 - 3 = 15 - 3

2x = 12

(2x)/2 = 12/2

x = 6

200

Solve for a:

(1/2)a + 5 = 18

a = 26

WORK

(1/2)a + 5 = 18

(1/2)a + 5 - 5 = 18 - 5

(1/2)a = 13

2*(1/2)a = 13*2

a = 26

300

Solve for t:

-t + 8 = 3

t = 5

WORK

-t + 8 = 3

-t + 8 - 8= 3 - 8

-t = -5 [which is the same thing as -1t = -5]

-1t/-1=-5/-1

t = 5

400

Solve for x:

(x – 7)/3 = -12

x = -29

WORK
(x – 7)/3 = -12
3*((x – 7)/3)= -12*3
x – 7 = -36
x – 7 + 7= -36 + 7
x = -29

500

Solve for x:

-24 = -10x + 3

x = 2.7

WORK
-24 = -10x + 3
-24 - 3= -10x + 3 - 3
-27 = -10x
-27/(-10)=-10x/(-10)
2.7 = x

Multi-Step Equations

100

Solve for m:

5 = 5m - 23 + 2m

m =4

WORK

5 = 5m - 23 + 2m

5 = 5m + 2m - 23

5 = 7m - 23

5 + 23 = 7m - 23 + 23

28 = 7m

28/7 = 7m/7

4 = m

200

Solve for x:

(x + 4) + 2x = 67

x = 21

WORK

(x + 4) + 2x = 67

x + 2x + 4 = 67 [addition is commutative]

3x + 4 = 67

3x + 4 - 4= 67 - 4

3x = 63

3x/3 = 63/3

x = 21

300

Solve for x:

-8(2x - 1) = 36

x = -7/4

WORK
-8(2x - 1) = 36
-16x + 8 = 36 [Distributive Property]
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4

400

Solve for x:

3.5 - 0.02x = 1.24

x = 113

WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113

500

Solve for x:

(3x)/4 + x/3 =10

3x/4 - x/3 = 10

[remember what fractions really look like?]

x = 24

WORK

3x/4 - x/3 = 10

9x/12 - 4x/12 = 10 [write fractions/common denominator]

5x/12 = 10

12*(5x/12) = 10*12

5x/5 = 120/5

x = 24

Variables on Both Sides

100

Solve for b:

3b - 4 = b + 2

b = 3

WORK

3b - 4 = b + 2

3b - 4 + 4 = b + 2 + 4

3b = b + 6

3b - b = b - b + 6

2b = 6

2b/2 = 6/2

b = 3

200

Solve for x:

5x + 2 = 2x + 14

x = 4

WORK

5x + 2 = 2x + 14

5x + 2 - 2 2x + 14- 2

5x = 2x + 12

5x - 2x = 2x - 2x + 12

3x = 12

3x/3 = 12/3

x = 4

300

Solve for p:

1.5p = 1.25p + 8

p = 32

WORK

1.5p = 1.25p + 8

1.5p - 1.25p = 1.25p - 1/25p + 8

0.25p/0.25 = 8/0.25

p = 32

400

Solve for x:

2(5x - 1) = 3(x + 11)

x = 5

WORK

2(5x - 1) = 3(x + 11)

10x - 2 = 3x + 33 [Distribute]

10x - 3x - 2 = 3x - 3x + 33

7x - 2 + 2 = 33 + 2

7x/7 = 35/7

x = 5

500

Solve for x:

9m - 4 = -3m + 5 + 12m

NO SOLUTION

-4 = 5

WORK

9m - 4 = -3m + 5 + 12m

9m - 4 = -3m + 12m + 5

9m -9m - 4 = 9m -9m + 5

-4 = 5 <~~~NO! So, No Solution!

Mixed Bag

100

What is the reciprocal of -4/5

-5/4

200

-12x + 4y = 20

solve the literal equation for y

y=5+3x

300

Back in the Stone Ages, cell phone bills were based on a flat monthly fee and the number of minutes used.  in the equation c = 0.07m + 29.99, what does the variable m represent?

(your answer is words, not a number)

m stands for the number of minutes used

400

Solve in terms of C

F = 9/5C +32

9/5(F-32)

500

-9x + 7 > -3x - 5

x<2