Question

Ecuaciones de desigualdad:

a) x-9≤8x-1
b) 2x-4+6x<10x-7
c) 0.6x+3.4≤8.4+0.1x
d) 4(x-3)-8≤5-x
e) (8x+1)(x-7)≥(2x-3)(4x+5)
f) x(x+12)>(x-4)²
g) (5−1)/3>3

Answer 1

a) x-9≤8x-1 = -7x≤8 = 7x≥-8 = x≥-8/7
b) 2x-4+6x<10x-7 = -2x<-3 = 2x>3 = x>3/2
c) 0.6x+3.4≤8.4+0.1x = 0.5x≤5 = x≤5/0.5 = x≤10
d) 4x-12-8≤5-x = 5x≤25 = x≤25/5 = x≤5
e) 8x²-56x+x-7≥8x²+10x-12x-15 = -53x≥-8 = 53x≤8 = x≤8/53
f) x²+12x>x²-8x+16 = 20x>16 = x>16/20 = x>4/5
g) (5x-1)/3>3 = 5x-1>9 = 5x>10 = x>10/5 = x>2