-5<2x+1<-1 - Math Central

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Question from Rahul:

How does -5<2x+1<-1 changes to 1<|2x+1|<5. What is the rule?
Can we apply absolute value function throughout the first inequality i.e. can we say |-5|<|2x+1|<|-1|. But then it becomes 5<|2x+1|<1 which is impossible because 5 is not less than 1.

Hi Rahul,

Since $2x - 1 < -1, 2x - 1$ is negative. Hence taking the absolute value of $2x - 1$ is equivalent to multiplying by $-1.$ When you multiply both sides of an inequality by a negative the inequality changes direction.

Penny

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