Question

Resolva as inequações:
A) x - 3 menor ou igual a -x +5
B) -2 (x-1) +4x menor ou igual a -10
C) x-1 sobre 3 - x-2 sobre 2 menor ou igual a 2
D) -1 < 2x +3

Answer 1

a. $x - 3 \leq - x + 5 = x + x \leq + 5 + 3 = 2x \leq 8 = x \leq \frac{8}{2} = x \leq 4$.
b. $-2 (x - 1) + 4x \leq -10 = -2x + 2 + 4x \leq -10 = 2x + 2 \leq -10 = 2x \leq -10 - 2 = 2x \leq -12 = x \leq \frac{-12}{2} = x \leq -6$
c. $\frac{x-1}{3} - \frac{x-2}{2} \leq 2 = \frac{2x-2-3x-6}{6} \leq 2= \frac{-x-8}{6} \leq 2 = -x-8 \leq 12 = -x \leq 12 + 8 = -x \leq 20 = x \geq 20$
d. $-1 < 2x +3 = 2x >-1 - 3 = 2x >-4 = x > \frac{-4}{2} = x > -2$

Answer 2

a)
x-3 $\leq$ -x+5
2x $\leq$ 8
x $\leq$ 4

b)
-2(x-1) $\leq$ -10
-2x+2 $\leq$ -10
-2x $\leq$ -12        .(-1)
2x $\geq$ 12
x $\geq$ 6

c) 
x-1/3 - x-2/2 $\leq$ 2
mmc= 6
(x-1).2-(x-2).3 $\leq$ 2
2x-2-3x+6 $\leq$ 2
-x $\leq$ 2-4    .(-1)
x ≤ 2

d)
-1 < 2x +3
2x>-4
x > -2