Question

16 va rog dau coroana

Answer 1

Bună! ⭐

__________

16) Determinați numerele întregi x care verifică relația:

a) |x-3|<4     b) |-2x+1|≤5      c) |2-3x|≤4

Rezolvare:

$a) |x-3|<4 => \left \{ {{-x+3<4} \atop {x-3<4}} \right. => \left \{ {{x>-1} \atop {x<7}} \right. =>$ x ∈ {0, 1, 2, 3, 4, 5, 6}

$b) |-2x+1|\leq 5 => -5\leq -2x+1\leq 5 /-1 => -6\leq -2x\leq 4 /:(-2) => 3\geq x\geq -2 =>$

x ∈ {-2, -1, 0, 1, 2, 3}

$c) |2-3x|\leq 4 => -4\leq 2-3x\leq 4/-2 => -6\leq -3x\leq 2/: (-3) => 2\geq x\geq -\frac{2}{3} =>$

x ∈ {0, 1, 2}