a)
[tex] | \frac{1}{2} x - 2.5 | = |7 \frac{1}{2} - \frac{3}{4} x| \\ | \frac{1}{2} x - \frac{5}{2} | = | \frac{15}{2} - \frac{3}{4} x | \\ [/tex]
CAZUL I
[tex] \frac{1}{2}x - \frac{5}{2} = \frac{15}{2} - \frac{3}{4} x \\ 2x - 10 = 30 - 3x \\ 2x + 3x = 30 + 10 \\ 5x = 40 \\ x = \frac{40}{5} = 8[/tex]
CAZUL II
[tex] \frac{1}{2} x - \frac{5}{2} = - ( \frac{15}{2} - \frac{3}{4} x) \\ \frac{1}{2} x - \frac{5}{2} = - \frac{15}{2} + \frac{3}{4} x \\ 2x - 10 = - 30 + 3x \\ 2x - 3x = - 30 + 10 \\ - x = - 20 \\ x = 20[/tex]
deci S= (8, 20)
b)
2x-1/5 =7 =>înmulțim ambele parti ale ecuației cu 5
2x-1=35
2x=35+1
2x=36
x=36/2
x=18
c)
(2/3)^x ÷ (2/3)^3=16/81 ×(2/3)^5
(2/3)^x-3= (2/3)^4 × (2/3)^5
(2/3)^x-3=(2/3)^9
x-3=9
x=9+3
x=12
d)
3+2/5 ×(3x-1 /8 +5x+1 /4)=x-1 /2 +1/3 ×7x+3 /2
3+ 3x-1 /20 + 5x+1 /10= x-1 /2 +7x+3 /6
(înmulțim ambele părți ale ecuației cu 60)
180+3(3x-1)+6(5x+1)=30(x-1)+10(7x+3)
180+9x-3+30x+6=30x-30+70x+30
180-3+6+30=-9x-30x+30x+70x
-183=-61x
183=61x
x= 183/61
x=3
