a) Solution for x:
x = {x / -3 ≤ x ≥ 2; x≠-2;1)
Interval notation:
(-∞, -3] ∪ (-2, 1) ∪ [2, +∞)
Step-by-step explanation:
Rational Inequality is inequality with rational numbers or expressions.
The symbols in inequality are:
Less than (<)
Greater than (>)
Less than or equal to (≤)
Greater than or equal to (≥)
In fraction or rational expression, the denominator is not 0. A zero-denominator renders the expression undefined.
Given:
(x+3)(x-2)/(x+2)(x-1)≥0
The rational expression:
Numerator: (x+3)(x-2)
Denominator: (x+2)(x-1) where x ≠ -2 and x ≠ 1 because the values -2 or +1 will make the expression undefined
Find the solution for x by equation the factors in enumerator to 0:
x+3 ≥ 0
x ≥ -3
x ≤ -3
x - 2 ≥ 0
x ≥ 2
But:
x ≠ -2
x ≠ 1
Hence:
Solution for x:
x = {x / -3 ≤ x ≥ 2; x≠-2;1)
Interval notation:
(-∞, -3] ∪ (-2, 1) ∪ [2, +∞)
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b) Take the root of both sides and solve
Inequality Form:
− 4 ≤ x < 2 or x ≥ 3
Interval Notation:
[ − 4 , 2 ) ∪ [ 3 , ∞ ]
