Question

7. Determine a solução de cada uma das inequações. a) 2 + 5x < -10 + 2x b)-3(y - 1)2-11 - 4y c) -9 + y < 2(y + 6) + 10 3(x + 4) d) x- 20 2.

Por favor, me ajudem!​

Answer 1

Resposta:

a) 2 + 5x < - 10 + 2x

2 + 5x - 2 < - 10 + 2x - 2

5x < 2x - 12

5x - 2x + 2x < 0

5x < 2x - 12 - 2x

3x < - 12

- 12:3

x < - 4

b) - 3( y - 1 ) ≥ - 11 - 4y

- 3y + 3 ≥ - 11 - 4y

- 3y + 3 - 3 ≥ 0

- 3y ≥ - 11 - 4y - 3

- 3y ≥ - 4y - 14

- 3y + 4y ≥ 14 + 4y

y ≥ - 14

c) - 9 + y < 2 ( y + 6 ) + 10

2 ( x + 6 ) + 10 > - 9 + y

2 ( x + 6 ) + 10 - 10 > 0

2 ( x + 6 ) > - 9 + y - 10

2 ( x + 6 ) > y - 19

$\frac{2(x+6)}{2} >\frac{y}{2} -\frac{19}{2}$

$x+6>\frac{y-19}{2}$

$x+6-6>\frac{y-19}{2} -6$

$x>\frac{y-19}{2} -6$

$x-\frac{3(x+4)}{2} \geq 0\\\\x*2-\frac{3(x+4)}{2} *2\geq 0*2\\\\x*2-3(x+4)\geq 0\\\\-x-12\geq 0\\\\-x-12+12\geq 0\\\\-x\geq 0+12\\\\-x\geq 12\\\\(-x)(-1)\leq 12(-1)\\\\x\leq -12$