Question

15.
a) 2(x+3)=10
b) 3 (x-1) +2 = 8
c) 2(13 - x ) - 9 =1
d) 3 (1-x) +2 = -7
e) 3(x+3)=2(x+4)+x+1
f) 4(3x+2)+5(2x+3)=-(2x+13)
g) 4(x-2)-2(x-4)=5(x+1)-3x
h)2(x-4)=2(2x-1)+6(x+1)

12.

a) 1/2y+3=7
b) 3/5y +2/5=4
c) 3(y+2)=5
d) 7(y+3)=5y+2+2y
e) y/2+1/3=7/6
f) y+3/2-(1-y)=3,5
g)1/5(y-3)-2/3(y-3/5)+1/3=2/5-1/3(2y-3)
h)2y+4/4=1/2y+1
i)y-2/3+1/15-2y-5/3=8-4y/5
j) y-5/2+2y+3/5+1/3=y+7/15+y/2

Answer 1

15.
a) 2(x+3)=10
2x+6=10
2x=10-6
2x=4/:2
x=2

b) 3 (x-1) +2 = 8
3x-3+2=8
3x=8+3-2
3x= 9/:3
x=3

c) 2(13 - x ) - 9 =1
26-2x-9=1
-2x=1+9-26
-2x=-16/ :(-2)
x=8

d) 3 (1-x) +2 = -7
3-3x+2 =-7
-3x=-7-3-2
-3x = -12 / :(-3)
x=4

e) 3(x+3)=2(x+4)+x+1
3x+9 = 2x+8+x+1
3x-2x-x = 1+8-9
0=0

f) 4(3x+2)+5(2x+3)=-(2x+13)
12x+8+10x+15 = -2x-13
12x+10x+2x = -13-8-15
24x = -36 / :24
x= -1 ½

g) 4(x-2)-2(x-4)=5(x+1)-3x
4x-8-2x+8=5x+5-3x
4x-2x-5x+3x = 5+8-8
0=5

h)2(x-4)=2(2x-1)+6(x+1)
2x-8=4x-2+6x+6
2x-4x-6x = -2+6+8
-8x = 12 / :(-8)
x= -1½

12.

a) 1/2y+3=7
1/2 y = 7-3
1/2 y = 4 / *2
y=8

b) 3/5y +2/5=4 / *5
3y+2 = 20
3y = 20-2
3y = 18 / :3
y=6

c) 3(y+2)=5
3y+6=5
3y = 5-6
3y = -1 / :3
y = -⅓

d) 7(y+3)=5y+2+2y
7y+21=5y+2+2y
7y-5y-2y = 2-21
0= -19

e) y/2+1/3=7/6 /*6
3y+2 = 7
3y = 7-2
3y = 5 / :3
y = 1 ²/₃

f) y+3/2-(1-y)=3,5 / *2
y+3-2+2y = 7
y+2y = 7-3+2
3y = 6 / :3
y=2

g)1/5(y-3)-2/3(y-3/5)+1/3=2/5-1/3(2y-3)
1/5y- 3/5 - 2/3y + 2/5 + 1/3 = 2/5 + 2/3 y +1 / *15
3y+9 -10y +6 +5 = 6+10y+15
3y-10y-10y = 6+15-9-6-5
-23y = 1 / (-23)
y = - 1/23

h)2y+4/4=1/2y+1 / *4
2y+4 = 2y+4
2y-2y = 4-4
0=0

i)y-2/3+1/15-2y-5/3=8-4y/5 / *15
5(y-2) +1-5(2y-5) = 3(8-4y)
5y-10+1-10y+25 = 24+12y
5y-10y-12y = 24+10-1-25
-17y = 8 / :(-17)
y = -8/17

j) y-5/2+2y+3/5+1/3=y+7/15+y/2 / *30
15(y-5) + 6(2y+3) + 10 = 2(y+7) + 15y
15y-75 +12y+18+10 = 2y+14+15y
15y+12y-2y-15y = 14+75-18-10
10y = 61 / :10
y= 6,1

Answer 2

15.
a) 2(x+3)=10
2x+6 = 10
2x = 10-6
2x = 4 /:2
x = 2

b) 3 (x-1) +2 = 8
3x-3+2 = 8
3x = 8+3-2
3x = 9 /:3
x = 3

c) 2(13 - x ) - 9 =1
26 -2x -9 =1
-2x = 1+9-26
-2x = -16 /:(-2)
x = 8

d) 3 (1-x) +2 = -7
3-3x+2 = -7
-3x = -7-2-3
-3x = -12 /:(-3)
x = 4

e) 3(x+3)=2(x+4)+x+1
3x+9 = 2x+8+x+1
3x-2x-x = 8+1-9
0x = 0 równanie tożsamościowe

f) 4(3x+2)+5(2x+3)=-(2x+13)
12x+8+10x+15 = -2x-13
12x+10x+2x = -13-15-8
24x = -36 /:24
x = - 3/2

g) 4(x-2)-2(x-4)=5(x+1)-3x
4x-8-2x+8 = 5x+5-3x
4x-2x+3x-5x = 5-8+8
0x = 5 równanie sprzeczne

h)2(x-4)=2(2x-1)+6(x+1)
2x-8 = 4x -2+6x+6
2x-4x-6x = 6-2+8
-8x = 12 /:(-8)
x = - 3/2


12.
a) 1/2y+3=7
1/2y = 7-3
1/2y = 4 /:1/2
y = 8

b) 3/5y +2/5=4
3/5y = 4-2/5
3/5y = 18/5 /:3/5
y = 6

c) 3(y+2)=5
3y+6 = 5
3y = 5-6
3y = -1 /:3
y = -1/3

d) 7(y+3)=5y+2+2y
7y+21 = 5y+2+2y
7y-2y-5y = 2-21
0y = -19 równanie sprzeczne

e) y/2+1/3=7/6 /*6
3y+2 = 7
3y = 7-2
3y = 5
y = 5/3

f) y+3/2-(1-y)=3,5
y+3/2-1+y = 3,5
2y = 3,5+1-3/2
2y = 3
y = 3/2

g)1/5(y-3)-2/3(y-3/5)+1/3=2/5-1/3(2y-3)
1/5y-3/5-2/3y+2/5+1/3 = 2/5-2/3y+1
1/5y-2/3y+2/3y = 1+2/5-1/3-2/5+3/5
1/5y = 19/15 /:1/5
y = 19/3

h)2y+4/4=1/2y+1
2y+1 = 1/2y+1
2y-1/2y = 1-1
3/2y = 0
y = 0

i)y-2/3+1/15-2y-5/3=8-4y/5 /*15
15y-10+1-30y-25 = 120-12y
15y-30y+12y = 120+25-1+10
-3y = 154
y = -154/3

j) y-5/2+2y+3/5+1/3=y+7/15+y/2 /*30
30y-75+60y+18+10 = 30y+14+15y
30y+60y-30y-15y = 14-10-18+75
45y = 61
y = 61/45