Bonsoir !!
-4 < b < -2
0.1 < a < 0.3
1.
a) a + b
-4 + 0.1 < a + b < -2 + 0.3
-3.9 < a + b < -1.7
b) 5a - 2b
0.1 < a < 0.3
0.5 < 5a < 1.5 ... ( 1 )
4 < -2b < 8 ... ( 2 )
( 1 ) + ( 2) ... 0.5 + 4 < 5a - 2b < 1.5 + 8
4.5 < 5a - 2b < 9.5
c) a × b
-4 × 0.1 > a × b > -2 × 0.3
-0.4 > a × b > -0.6
d) a/b
0.1 < a < 0.3 ... ( 1 )
-4 < b < -2
1/(-2) < 1/b < 1/(-4) ...( 2 )
( 1 ) × ( 2 ) ... 0.1 × (1/(-2) < a × 1/b < 0.3 × (1/(-4)
0.1/(-2) < a/b < 0.3/(-4)
e) 3b² - 1
-4 < b < -2
(-2)² < b² < (-4)²
4 < b² < 16
12 < 3b² < 48
12 - 1 < 3b² - 1 < 48 - 1
11 < 3b² - 1 < 47
f) a / (a - b)
0.1 < a < 0.3 ... ( 1 )
0.1 - (-4) < a - b < 0.3 - (-2)
4.1 < a - b < 2.3
1/2.3 < 1/(a - b) < 1/4.1 ... ( 2 )
( 1 ) × ( 2 )... 0.1/2.3 < a/(a - b) < 0.3/4.1
2) 2 < y < 4
2 < x < 4
a) x - y ou x + (-y)
-4 < -y < -2
2 + (-4) < x + (-y) < 4 + (-2)
-2 < x - y < 2
b) x - y + x/y
-2 < x - y < 2 ... ( 1 )
1/4 < 1/y < 1/2
2/4 < x/y < 4/2
1/2 < x/y < 2 ... ( 2 )
( 1 ) + ( 2 ) ... -2 + 1/2 < x - y + x/y < 2 + 2
-3/2 < x - y + x/y < 4
