Question

rezolvați inecuațiile:
a)4x-5≤3x-2 ,x € N
b)7x+9>3x-7 ,x € Z_
c)2|x-1|+3x≤3(x+2) ,x€ N*
d)3|x+2|-2x≤2(2-x)+5, x € Z_
(Z_ :Z minus) ​

Answer 1

Răspuns:

a)

\begin{gathered}4x−5 < 3x− 2 \\ 4x - 3x < - 2 + 5 \\\implies x < 3\end{gathered}

4x−5<3x−2

4x−3x<−2+5

⟹x<3

x ∈ N => x ∈ {0; 1; 2}

b)

\begin{gathered}7x+9 > 3x-7 \\ 7x - 3x > - 7 - 9 \\ 4x > - 16 \\ \implies x > - 4\end{gathered}

7x+9>3x−7

7x−3x>−7−9

4x>−16

⟹x>−4

x ∈ Z => x ∈ {-3; -2; -1; 0; 1; ...}

c)

\begin{gathered}2x - 1 + 3x \leqslant 3(x + 2) \\ 5x - 1\leqslant 3x + 6 \\ 5x - 3x \leqslant 6 + 1 \\ 2x \leqslant 7 \\ x \leqslant \frac{7}{2} \iff x \leqslant 2 \frac{1}{2} \end{gathered}

2x−1+3x⩽3(x+2)

5x−1⩽3x+6

5x−3x⩽6+1

2x⩽7

x⩽

2

7

⟺x⩽2

2

1

x ∈ N* => x ∈ {1; 2}

d)

\begin{gathered}3x +21-2x \leqslant 2(2-x)+5 \\ x + 21 \leqslant 4 - 2x + 5 \\ x + 2x \leqslant 9 - 21 \\ 3x \leqslant 12 \implies x \leqslant 4\end{gathered}

3x+21−2x⩽2(2−x)+5

x+21⩽4−2x+5

x+2x⩽9−21

3x⩽12⟹x⩽4

x ∈ Z => x ∈ {...; -1; 0; 1; 2; 3; 4}