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14 votes
14 votes
6x-5 < -17 or 4x + 5 ≥ 13
What is the solution

User Artur  Dumchev
by
2.9k points

1 Answer

11 votes
11 votes

Answer:

x < -2 or x ≥ 2

In interval notation:
(- ∞, 2) ∪ [2, ∞) Notice square bracket next to 2 because the second inequality is a ≥inequality whereas the first inequality is a < inequality

Explanation:

First inequality: 6x - 5 < - 17

Add 5 to both sides:
6x < -17 + 5
6x < -12

Divide both sides by 2 to get
x < -2

In interval notation it is (-∞ , -2) () means neither value is included

Second inequality: 4x + 5 ≥ 13
Subtract 5 from both sides:
4x ≥ 13 -5
4x ≥ 8

Divide both sides by 4:
x ≥ 2

In interval notation [2, ∞) Note square bracket next to 2 which means that value is included. ∞ is never included so it is always accompanied by a ( or ) bracket

Hence we have x < -2 or x >= 2

In interval notation we have (- ∞, 2) ∪ [2, ∞) where the symbol ∪ represents set union which is equivalent to an or

See the attached figure for visual explanation


User Nitrodist
by
2.9k points
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