Răspuns:
Explicație pas cu pas:
M = {-3, 0, 1, 2, -1}
a)
x + 2 ≤ 3
x ≤ 3 - 2
x ≤ 1
{-3, 0, 1, -1}
b)
-x + 5 > -7
x < 5 + 7
x < 12
{-3, 0, 1, 2, -1}
c)
-3x ≥ -3
3x ≤ 3
x ≤ 3 : 3
x ≤ 1
{-3, 0, 1, -1}
d)
-3x + 2 > -4
-3x > -4 - 2
-3x > -6
3x < 6
x < 6 : 3
x < 2
{-3, 0, 1, -1}
e)
4x + 1 ≤ -2x + 1
4x + 2x ≤ 1 - 1
6x ≤ 0
x ≤ 0 : 6
x ≤ 0
{-3, 0, -1}
f)
-2x + 1 ≥ -x - 5
-2x + x ≥ -5 - 1
-x ≥ -6
x ≤ 6
{-3, 0, 1, 2, -1}
Explicație pas cu pas:
a)
[tex]x + 2 \leqslant 3 \iff x \leqslant 3 - 2 \\ \implies x \leqslant 1[/tex]
M = {-3, -1, 0, 1}
b)
[tex] - x + 5 > - 7 \iff - x > - 7 - 5 \\ - x > - 12 \implies x < 12[/tex]
M = {-3, -1, 0, 1, 2}
c)
[tex] - 3x \geqslant - 3 \iff 3x \leqslant 3 \\ \implies x \leqslant 1[/tex]
M = {-3, -1, 0, 1}
d)
[tex] - 3x + 2 > - 4 \iff - 3x > - 4 - 2 \\ - 3x > - 6 \iff 3x < 6 \\ \implies x < 2[/tex]
M = {-3, -1, 0, 1}
e)
[tex]4x + 1 \leqslant - 2x + 1 \iff 4x + 2x \leqslant 1 - 1 \\ 6x \leqslant 0 \implies x \leqslant 0[/tex]
M = {-3, -1, 0}
f)
[tex]- 2x + 1\geqslant - x - 5 \iff - 2x + x \geqslant - 5 - 1 \\ - x \geqslant - 6 \implies x \leqslant 6[/tex]
M = {-3, -1, 0, 1, 2}