Onevariable compound inequality
1≤ 3 + 2x < 17 is a compoundinequalitysinceit can be expressed as two separate inequalities thus 1 ≤ 3 + 2xand3 + 2x < 17. This will also result in two solutions as follows:
1≤ 3 + 2x 3 + 2x < 17
2≤ 2x 2x < 20
1≤ x x < 10
T his means that the value of x is greater than one but lessthan 10. The solutions can also be written as a compound inequalitythus 1 ≤ x < 10. This can also be written as [1,∞] ∩ (∞,10]. The solution is an intersectionbetween the separate solutions of the two inequalities handledseparately. They solutions can also be represented on the lineardiagram as shown below.

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Thefollowing inequalities will give the orcondition: 7 – x ≥ 6 or7x – 1 > 27
Therefore,solving the two inequalities separately gives 7 – x ≥6 7x – 1 > 27
x≥ 1 7x > 28
x≤ 1 x > 4
Thereis no intersectionin the solutions. This means that the value of x must be the less orequal to one orthe value of x must be greater than 4. The graphical representationof the solutions will be as given number line drawn below. It shouldbe noted that the solution set is a unionof the two solutions and can be written as [∞,1] U (4,∞].

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