QuestionSolve the inequality $|2x-5|-3<-7$ and identify the solution set: $-5<x<-1$ , $x<-5$ or $x>-1$ , $\varnothing$ , or $R$ .

Studdy Solution

STEP 1

Assumptions1. The given inequality is $|x-5|-3<-7$ . We need to find the set that describes all the solutions to the inequality

STEP 2

First, we simplify the inequality by adding to both sides to isolate the absolute value.
$|2x-5|-+<-7+$

STEP 3

After simplifying, we get $|2x-5|<-$

STEP 4

An absolute value of a number is always non-negative. It can be zero or positive, but never negative. Therefore, there are no real numbers that can make the inequality $|2x-|<-4$ true.

STEP 5

So, the solution to the inequality $|2x-5|-3<-7$ is the Empty Set, $\varnothing$ .

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QuestionSolve the inequality $|2x-5|-3<-7$ and identify the solution set: $-5<x<-1$ , $x<-5$ or $x>-1$ , $\varnothing$ , or $R$ .

Studdy Solution

STEP 1

Assumptions1. The given inequality is $|x-5|-3<-7$ . We need to find the set that describes all the solutions to the inequality

STEP 2

First, we simplify the inequality by adding to both sides to isolate the absolute value.
$|2x-5|-+<-7+$

STEP 3

After simplifying, we get $|2x-5|<-$

STEP 4

An absolute value of a number is always non-negative. It can be zero or positive, but never negative. Therefore, there are no real numbers that can make the inequality $|2x-|<-4$ true.

STEP 5

So, the solution to the inequality $|2x-5|-3<-7$ is the Empty Set, $\varnothing$ .

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QuestionSolve the inequality ∣2x−5∣−3<−7|2x-5|-3<-7∣2x−5∣−3<−7 and identify the solution set: −5<x<−1-5<x<-1−5<x<−1, x<−5x<-5x<−5 or x>−1x>-1x>−1, ∅\varnothing∅, or RRR.

Studdy Solution

STEP 1

Assumptions1. The given inequality is ∣x−5∣−3<−7|x-5|-3<-7∣x−5∣−3<−7 . We need to find the set that describes all the solutions to the inequality

STEP 2

First, we simplify the inequality by adding to both sides to isolate the absolute value.∣2x−5∣−+<−7+|2x-5|-+<-7+∣2x−5∣−+<−7+

STEP 3

After simplifying, we get∣2x−5∣<−|2x-5|<-∣2x−5∣<−

STEP 4

An absolute value of a number is always non-negative. It can be zero or positive, but never negative. Therefore, there are no real numbers that can make the inequality ∣2x−∣<−4|2x-|<-4∣2x−∣<−4 true.

STEP 5

So, the solution to the inequality ∣2x−5∣−3<−7|2x-5|-3<-7∣2x−5∣−3<−7 is the Empty Set, ∅\varnothing∅.

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Studdy solves anything!

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QuestionSolve the inequality $|2x-5|-3<-7$ and identify the solution set: $-5<x<-1$ , $x<-5$ or $x>-1$ , $\varnothing$ , or $R$ .

Assumptions1. The given inequality is $|x-5|-3<-7$ . We need to find the set that describes all the solutions to the inequality

First, we simplify the inequality by adding to both sides to isolate the absolute value.
$|2x-5|-+<-7+$

After simplifying, we get $|2x-5|<-$

An absolute value of a number is always non-negative. It can be zero or positive, but never negative. Therefore, there are no real numbers that can make the inequality $|2x-|<-4$ true.

So, the solution to the inequality $|2x-5|-3<-7$ is the Empty Set, $\varnothing$ .