Question

ME AJUDEM URGENTE
Resolva as inequações:
a) 5x – 2.(x + 2) ≥ 1 – (3 – 4x)

b) 3(x - 1)/2 - x-1/4 ≤ 1/2

Answer 1

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

b) 3(x - 1)/2 - (x-1)/4 ≤ 1/2
(3x-3)/ 2 - (x-1)/4 ≤1/2 (faz mmc)
6x-6 -x+1 ≤ 2
5x-5≤2
5x≤7
x≤7/5

Answer 2

a)
5x-2(x+2)≥1-(3-4x)

5x-2x-4 ≥1-3+4x

5x-2x-4x ≥1-3+4

5x-6x≥5-3
-x ≥ 2
x ≤ -2
S={x∈R /x ≤ -2}

observe que quando o x for negativo troca-se o sinal
logo ≥ passa para ≤

b)

$\frac{3(x-1)}{2} - \frac{x-1}{4} \leq \frac{1}{2} \\ \\ mmc(2,4)=4 \\ \\ 6(x-1)-1(x-1) \leq 2 \\ \\ 6x-6-x+1 \leq 2 \\ \\ 6x-x \leq 2+6-1 \\ \\ 5x \leq 7 \\ \\ x \leq \frac{7}{5} \\ \\ S=\{x\in R/x \leq \frac{7}{5} \}$