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What is the solution to the compound inequality 3x − 8 ≥ −5 and 2x − 7 < 5?

x ≤ 1 and x > 6
1 ≤ x < 6
x > 1 and x > 6
1 < x < 6

2 Answers

1 vote

1<x<6 or its x>1 and x>6

User Hillkorn
by
8.0k points
2 votes

Answer:

The solution to the compound inequality is given by:


1\leq x<6

Explanation:

The compound inequality is given by:


3x-8\geq -5 and


2x-7<5

  • On solving the first inequality i.e.


3x-8\geq -5

on adding both side of the inequality by 8 we get:


3x\geq -5+8\\\\i.e.\\\\3x\geq 3

Now on dividing both side of the inequality by 3 we get:


x\geq 1

  • The second inequality is given by:


2x-7<5

On adding both side of the inequality by 7 we get:


2x<5+7\\\\i.e.\\\\2x<12

on dividing both side of the inequality by 2 we get:


x<6

Hence, the solution of the compound inequality is:


1\leq x<6

User Thenewbie
by
7.5k points

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