Green Team - Solving Equations

Equations with D.P.

100

3(5x+8) = 3x-2

x= -10

200

3(4b-1) = 7(2b-5)

b=16

300

5(n+3)-4(2n-9)=0

n=17

400

9z-2(z+8) = 5z-11

z=5/2 or 2 1/2 (2.5)

500

1 - 4(2a+3) = 5(a-2) - 3(a-1)

a= -2/5

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

[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!

Fractions and Equations

100

Solve:

12 + 2/5x = 16

x = 10

WORK

2/5x = 16-12

2/5x = 4

(5) 2/5x = 4(5)

2x = 20

x = 20/2

x = 10

200

Solve:

(3x-11)/7 -2 = 0

x = 25/3 or 8 1/3

WORK

(3x-11)/7 -2 = 0

(7) (3x-11)/7 = 2 (7)

3x-11 = 14 

3x=25

x = 25/3 = 8 1/3

300

Solve:

[3(5x-6)]/4 + 2 = 4x

x = -10

Work:

(4) [3(5x-6)]/4 + 2 = 4x (4)

3(5x-6)+8 = 16x

15x-18+8 = 16x

-10 = x

400

Solve

(y+9)/2 =(y-3)/4 - y/3

y = -9

WORK

(y+9)/2 =(y-3)/4 - y/3

(12) (y+9)/2 = (y-3)/4 - y/3 (12) 

6(y+9) = 3(y-3) -4y

6y+54 = 3y-9-4y

6y+54 = -9-y

7y=-63

y=-9

500

Solve

(4x+3)/5 - (7x-1)/3 = (2-19x)/10

x = -2

WORK

(30) (4x+3)/5 - (7x-1)/3 = (2-19x)/10 (30)

6(4x+3) - 10(7x-1) = 3(2-19x)

24x+18 - 70x +10 = 6 - 57x

-46x + 28 = 6 - 57x

11x=-22

x=-2