Download 1-1 linear equation

1-1 linear equation
3x-7
linear eq
-5x
linear eq
2x² -3x+9 non linear
Definition (linear equation)
ax+b
namber
‫عدد‬
vonable constant
‫مجهول‬
‫ثابت‬
2x+5 / 3x-9
‫ ) مجال‬Domain )
Find domain :
1) 2x+9 domain = R
2) x/2-3 domain = R
3) 1/x = 4/x-3
X=0
x-3=0
x=3
domain = R
[0,3] ‫ماعدا‬
Solve :
1) 3x-8=4
3x=4+8
3x/3 = 12/3
X=4
2) x/2 +3 = 6
x/2 = 6-3
x/2 = 3/1
x=6
3) 5+4(t-2) = 2(t+7) +1
5+4t-8 = 2t+14+1
-3+4t = 2t+15
-3+4t-2t = 15
4t-2t = 15+3
2t/2 = 18/2
T=9
4) 2/y + 5/2 = 3/3y -1/3
2/y -3/3y + 5/2 = -1/3
2/y -3/3y + 5/2 = -1/3
3*2/3*y – 3/3y = 2*1/2*3 – 5*3/2*3
6-3/3y = -2-15/6
3/3y - -17/6
-7*3y = 3*6
-51/-51y = 18/-51
Y= 18/-51
2(x+1)/3 = 1
1) R
2) 2x+2/3 = 1/1
2x+2 = 3
2x = 3 -2
2x/2 = 1/2
X= 1/2
Solve the domain :
11+3y = 5y -5
1) domain = R
2) 11+5 = 5y -3y
16/2 = 2y/2
Y=8
s.s {8}
4-3 (t+2) +t = 5 (t-1) -7t
1) domain = R
2) 4-3t-6+t = 5t-5-7t
3) 4-6+5 = 5t-7t+3t-t
3 = 8t – 8t
3 ≠ 0 no solution
5- 2x-1/4 = x+2/3
1) domain = R
2) 5 = x+2/3 + 2x-1/4
5 = 4(x+2)+3(2x-1)/3*4
5 = 4x+8+6x-3/12
5*12 = 4x+8+6x-3
60 = 4x+8+6x-3
60-8+3 = 4x+6x
55/10 = 10x/10
X = 55/10 = 5,5
s.s = {5,5}
x/5+3x-7/2 = 6x+5/4
1) domain = R
2) 2x+5 (3x-1)/(5)(2) = 6x+5/4
2x+15x-5/10 = 6x+5/4
4(2x+15x-5) = 10(6x+5)
8x+60x-20 = 60x+50
8x+60x-66x = 50+20
8x/8 = 70/8
X= 70/8
s.s = {70/8}
3(y-4)+2y = 18
1) domain = R
2) 3y-12+2y = 18
3y+2y = 18+12
5y = 30
5y/5 = 30/5
Y = 30/5 = 6
s.s = {6}
11+3y = 5y-5
11+5 = 5y-3y
16/8 = 8y/8
2=y
4-3 (t+2)+t = 5 (t-1) -7t
4-3t+6+t = 5t-5-7t
4+6+5 = 5t-t7+3t-t
15 = -2+2t
15-t
3 (y-4) +2y = 18
3y-12+2y = 18
3y+2y = 18+12
5y/5 = 30/5
Y=6