Question

Resolva as inequaçoes:
a) 5x-2(x+2)maior ou igual1-(3-4x)
b) 3(x+1)/2 - x-1/4 menor ou igual1/2
c) 5(3x+1)/2 - 3x/4 > 5(1-3x)/8 + 18/3

Answer 1

a)
5x - 2(x + 2) ≥ 1 - (3 - 4x)
5x - 2x - 4 ≥ 1 - 3 + 4x
3x - 4 ≥ - 2 + 4x
3x - 4x ≥ - 2 + 4
- x ≥ 2  ( - 1)
x ≤ - 2

{x ∈ R / x ≤ - 2}
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b)

3(x + 1)  -  (x - 1) ≤  1
   2               4        2

mmc (2,4) = 4

2.3(x + 1) - x + 1 ≤   2
          4                  4

6(x + 1) - x + 1 ≤ 2
6x + 6  - x + 1 ≤ 2
5x + 7 ≤ 2
5x ≤ 2 - 7
5x ≤  - 5
x ≤ - 5/5
x ≤ - 1

{x ∈ R / x ≤ - 1}
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c)
5.(3x +1) - 3x > 5.(1 - 3x) + 18
        2       4           8          3

12.5(3x + 1) - 6.3x > 3.5(1 - 3x) + 8.18
                24                        24

60(3x + 1) - 18x > 15(1 - 3x) + 144
180x + 60 - 18x > 15 - 45x + 144
162x + 60 > 159 - 45x
162x + 45x > 159 - 60
207x > 99
x >   99    : 9  =     11
       207   : 9         23

x > 11
      23

{x ∈ R / x > 11/23}

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mmc = 24

2,4,8,3: 2
1,2,4,3: 2
1,1,2,3: 2
1,1,1,3: 3
1,1,1,1      = 2.2.2.3 = 8.3 = 24

Answer 2

$a) 5x-2(x+2) \geq 1-(3-4x)\to \\\\ 5x-2x-4 \geq 1-3+4x\to \\\\ 5x-2x-4x \geq 1-3+4\to \\\\-x \geq 2(-1)\to \\\\ x \leq -2\\\\\\ S=\{xER|x \leq -2\}$



$b) \frac{3(x+1)}{2} - \frac{(x-1)}{4} \leq \frac{1}{2} \to mmc=4\\\\ 6(2x+2)-(x-1) \leq 2\to \\\\ 12x+12-x+1 \leq 2\to \\\\ 12x-x \leq 2-12-1\to \\\\ 11x \leq -11\to \\\\x \leq - \frac{11}{11} \to \\\\ x \leq -1\\\\\\\\ S=\{xER|x \leq -1\}$



c) 5(3x+1)/2- (3x)/4 > 5(1-3x)/8 + 18/3--->
(15x+5)/2 - (3x)/4 > (5-15x)/8 + 6--->
$60x+20-6x \ \textgreater \ 5-15x+48\to \\\\ 60x-6x+15x\ \textgreater \ 5+48 -20 \to \\\\ 69x\ \textgreater \ 33 \to \\\\ x\ \textgreater \ \frac{33}{69} (simplifique\ por~3)\\\\ x\ \textgreater \ \frac{11}{23} \\\\\\\\ S=\{xER| x\ \textgreater \ \frac{11}{23} \}$