Răspuns:
3.
a) x < -2
b) y > -2
c) z ≤ -4
d) t ≥ -7/2
4.
a) x > 1
b) x < -30
c) x ≥ 1/7
d) x ≥ -17/7
Explicație pas cu pas:
3.
a) 2x+3 < x+1 ⇔ 2x-x<-3+1 ⇔ x<-2
b) -3y+7 > -5y+3 ⇔ -3y+5y > -7+3 ⇔ 2y > -4 ⇔ y > -4/2 ⇔ y > -2
c) -10 ≥ 2(z+1)+z ⇔ -10 ≥ 2z+2+z ⇔ -10 ≥ 3z+2 ⇔ -3z ≥ 10+2 ⇔ -3z ≥ 12 ⇔ 3z ≤ -12 ⇔ z ≤ -4
d) [tex]0,5t + \frac{1}{2} \leq 1,5t +4[/tex] ⇔ [tex]0,5t-1,5t \leq -\frac{1}{2} +4[/tex] ⇔ [tex]-t\leq \frac{7}{2}[/tex] ⇔ [tex]t\geq -\frac{7}{2}[/tex]
4.
a) [tex]\frac{2}{3} x - \frac{1}{5} > \frac{7}{15}[/tex] ⇔ [tex]\frac{2}{3} x > \frac{3}{15} + \frac{7}{15}[/tex] ⇔ [tex]\frac{10}{15} x > \frac{10}{15}[/tex] ⇔ x > 1
b) 1,3x - 13 < 2x +8 ⇔ -0,7x < 13+8 ⇔ -0,7x < 21 ⇔ [tex]x < -\frac{21}{0,7}[/tex] ⇔ x < -30
c) [tex]\frac{-2x+1}{5} \geq \frac{-5x+1}{2}[/tex] ⇔ -4x+2 ≥ -25x+5 ⇔ -4x+25x ≥ -2+5 ⇔ 21x ≥ 3 ⇔ [tex]x\geq \frac{1}{7}[/tex]
d) [tex]\frac{4(x+3)}{-3} \leq \frac{2x-2}{9}[/tex] ⇔ [tex]\frac{-12x - 36}{9} \leq \frac{2x-2}{9}[/tex] - am trecut semnul - la numarator si am adus la numitor comun cu membrul drept
-12x - 36 ≤ 2x-2 (fiind numitor comun, inegalitatea se transfera asupra numaratorilor)
-12x-2x ≤ 36-2 ⇔ -14x ≤ 34 ⇔ 7x ≥ -17 ⇔ [tex]x\geq \frac{-17}{7}[/tex]
