Question

Determine a solução das inequações do 1° grau
A) (x+1)(x+1)-(x-1)(x-1)<8
B) 5x-(x+3)2 >/ (2x+9)-x2
C) x-5/4 - x/20 > 4-x/5
D) 1-x/2 + x-2/6 >/ 2x+1/2

Answer 1

A) (x+1)(x+1)-(x-1)(x-1)  <  8
x²+2x+1 -(x²-2x+1)  <  8
x²-x²+2x+2x+1-1  <  8
4x  <  8  
x  <  2

B) 5x-(x+3)2   >/   (2x+9)-x2
5x-(x²+6x+9)  >/   2x+9 -x²
5x-x²-6x-9+x²-2x    >/    9
-3x    >/   18
x   >/   -6

C) x-5/4 - x/20   >   4-x/5
x- x/20 + x/5   >   5/4 + 4
20x/20 -x/20+4x/20  >  21/4
23x/20  >  21/4
x  >  105/23

D) 1-x/2 + x-2/6   >/   2x+1/2
4/6 +x/2 -2x   >/   1/2
-3x/2   >/   1/2-4/6
-3x/2   >/   -1/6    *(-1)
3x/2   \<   1/6
x   \<  1/9