Question

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Answer 1

ex.1
a) 3x-6≤0
3x≤6
x≤6/3
x≤2
x∈(-∞,2]

b) 4^(x+1)=16
4^(x+1)=4²
x+1=2
x=2-1
x=1

ex.2
a) Ix-3I=5
x-3=5
x=5+3
x=8
x-3=-5
x=-5+3
x=-2
S={-2,8}

b) Ix-3I+Ix²-9)=0
x₁=3
x²-9=0
x²=9
x₂=√9=3
x₃=-√9=-3
x         -∞             -3             3               +∞
x-3     - - - - - - - -- - - - -- - - - -0++++++++++
x²-9    +++++++++0- - - - - - --0+++++++++++
f(x)     - - - - - - - - - 0+++++++0++++++++++
daca∈(-∞,-3)=D1
-x+3+x²-9=0
x²-x-6=0
Δ=1+24=25
x₁=(1-5)/2=-4/2=-2∈D1
x2=(1+5)/2=6/2=3∉D1
daca x∈[-3,3]=D2
-x+3-x²+9=0
-x²-x+12=0    inmultim -1
x²+x-12=0
Δ=1+48=49
x₁==(-1+7)/2=6/2=3∈D2
x₂=(-1-7)/2=-8/2=-4∉D2
daca ∈(3, +∞)=D3
x-3+x²-9=0
x²+x-12=0
x₁=3∉D3
x₂=-4∉D3
S={-2,3}

c) 5(x-6)-2x=x-38
5x-30-2x=x-38
3x-x=30-38
2x=-8
x=-8/2
x=-4

d)(x-4)²+(x-5)(x+5)=2(x+2)²+15
x²-8x+16+x²-25=4=2x²+8x+8+15
2x²-8x-9=2x²+8x+23
2x²-2x²-8x-8x=23+9
-16x=32     inmultim -1
16x=-32
x=-32/16=-2
x=-2

e) (2x-5)/3+(3x-5)/2=(4x-1)/4-5/12
4(2x-5)+6(3x-5)=3(4x-1)-5
8x-20+18x-30=12x-3-5
26x-50=12x-8
26x-12x=50-8
14x=42
x=42/14
x=3

ex.3
a) 5(x+3)-4(x-1)=3(x+9)
5x+15-4x+4=3x+27
x-3x=27-15-4
-2x=8    inmultim -1
2x=-8
x=-8/2
x=-4

b) 6(x-2)+1≤19
6x-12≤19-1
6x≤18+12
6x≤30
x≤30/5
x≤6
x∈N stelat
x={1,2,3,4,5,6}