Question

Resolva as seguintes inequacoes,em r
a)2x+1≤+6=
b)2-3x≥x+14=
c)2(x-3)maior q 3(1-x)=
d)3(1-2x)menor q 2(x+1)+x-7=

Answer 1

a)
2x + 1 ≤ 6
2x ≤ 6 - 1
2x ≤ 5
x ≤ $\frac{5}{2}$

b)
2 - 3x ≥ x + 14
- 3x - x ≥ 14 - 2
- 4x ≥ 12
x ≥ $\frac{12}{-4}$
x ≥ - 3

c)
2(x - 3) > 3(1 - x)
2x - 6 > 3 - 3x
2x + 3x > 3 + 6
5x > 9
x > $\frac{9}{5}$

d)
3(1 - 2x) < 2(x + 1) + x - 7
3 - 6x < 2x + 2 + x - 7
- 6x - 2x - x < 2 - 7 - 3
- 8x < - 8
x < $\frac{-8}{-8}$
x < 1

Answer 2

a)2x+1≤+6=  2x ≤ 6 - 1 ==> 2x ≤ 5 ==> x ≤ 5/2
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b)2-3x≥x+14=  - 3x - x ≥ 14 - 2 ==> - 4x ≥ 12(-1) ==> 4x ≤ - 12 ==> x ≤ - 3
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c)2(x-3)maior q 3(1-x)= 2x - 6 > 3 - 3x ==> 2x+3x > 3+6 ==> 5x>9 ==> x >9/5
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d)3(1-2x)menor q 2(x+1)+x-7= 3 - 6x < 2x + 2 + x - 7 ==> -6x-2x-x<2-7-3

- 9x < - 8(-1) ==> 9x > 8 ==> x > 8/9