(4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
(-x ≤ -5) ∩ (3x ≥ 15).
The inequality reverses in the left part since we are dividing
through by a negative number -1.
(x ≥ 5) ∩ (x ≥ 5).
Draw each part on a number line
-------------------------------@===========> That's x ≥ 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-------------------------------@===========> That's x ≥ 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Intersection ∩ means to use ONLY the part where the two
graphs overlap, that is, the part of the number line where
BOTH are true and darkened or shaded ===. @ means a darkened circle.
But they (overlap) intersect EVERYWHERE!!!
-------------------------------@===========>
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
So that is x ≥ 5, which in scientific notation is [5,oo)
where oo indicates "infinity".
Edwin
(4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
(-x ≤ -5) ∩ (3x ≥ 15).
The inequality reverses in the left part since we are dividing
through by a negative number -1.
(x ≥ 5) ∩ (x ≥ 5).
Draw each part on a number line
-------------------------------@===========> That's x ≥ 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-------------------------------@===========> That's x ≥ 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Intersection ∩ means to use ONLY the part where the two
graphs overlap, that is, the part of the number line where
BOTH are true and darkened or shaded ===. @ means a darkened circle.
But they (overlap) intersect EVERYWHERE!!!
-------------------------------@===========>
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
So that is x ≥ 5, which in scientific notation is [5,oo)
where oo indicates "infinity".
Edwin
