QuestionSolve the inequality: $-\frac{13}{4} < x < -\frac{5}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The problem is a compound inequality, which means that the solution will be a range of values for x that satisfy both inequalities. . The inequality symbols "<" mean "less than", so we are looking for values of x that are less than certain numbers.

STEP 2

First, let's look at the first inequality $-\frac{13}{4}<x$ This means that x is greater than -13/4.

STEP 3

Now, let's look at the second inequality $x<-\frac{5}{2}$ This means that x is less than -5/2.

STEP 4

The solution to the compound inequality is the intersection of the solutions to the two inequalities. In other words, the solution is the set of all x that satisfy both inequalities.

STEP 5

To find this intersection, we look for the values of x that are both greater than -13/4 and less than -5/2.

STEP 6

The solution to the compound inequality is the range of x values that satisfy both conditions. Since -13/4 is less than -5/2, there are no values of x that are both greater than -13/4 and less than -5/2.

STEP 7

Therefore, the solution to the compound inequality is the empty set, which means there are no values of x that satisfy the inequality.

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QuestionSolve the inequality: $-\frac{13}{4} < x < -\frac{5}{2}$ .

Studdy Solution

STEP 1

Assumptions1. The problem is a compound inequality, which means that the solution will be a range of values for x that satisfy both inequalities. . The inequality symbols "<" mean "less than", so we are looking for values of x that are less than certain numbers.

STEP 2

First, let's look at the first inequality $-\frac{13}{4}<x$ This means that x is greater than -13/4.

STEP 3

Now, let's look at the second inequality $x<-\frac{5}{2}$ This means that x is less than -5/2.

STEP 4

The solution to the compound inequality is the intersection of the solutions to the two inequalities. In other words, the solution is the set of all x that satisfy both inequalities.

STEP 5

To find this intersection, we look for the values of x that are both greater than -13/4 and less than -5/2.

STEP 6

The solution to the compound inequality is the range of x values that satisfy both conditions. Since -13/4 is less than -5/2, there are no values of x that are both greater than -13/4 and less than -5/2.

STEP 7

Therefore, the solution to the compound inequality is the empty set, which means there are no values of x that satisfy the inequality.

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QuestionSolve the inequality: −134<x<−52-\frac{13}{4} < x < -\frac{5}{2}−413​<x<−25​.

Studdy Solution

STEP 1

Assumptions1. The problem is a compound inequality, which means that the solution will be a range of values for x that satisfy both inequalities. . The inequality symbols "<" mean "less than", so we are looking for values of x that are less than certain numbers.

STEP 2

First, let's look at the first inequality−134<x-\frac{13}{4}<x−413​<xThis means that x is greater than -13/4.

STEP 3

Now, let's look at the second inequalityx<−52x<-\frac{5}{2}x<−25​This means that x is less than -5/2.

STEP 4

The solution to the compound inequality is the intersection of the solutions to the two inequalities. In other words, the solution is the set of all x that satisfy both inequalities.

STEP 5

To find this intersection, we look for the values of x that are both greater than -13/4 and less than -5/2.

STEP 6

The solution to the compound inequality is the range of x values that satisfy both conditions. Since -13/4 is less than -5/2, there are no values of x that are both greater than -13/4 and less than -5/2.

STEP 7

Therefore, the solution to the compound inequality is the empty set, which means there are no values of x that satisfy the inequality.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality: $-\frac{13}{4} < x < -\frac{5}{2}$ .

First, let's look at the first inequality $-\frac{13}{4}<x$ This means that x is greater than -13/4.

Now, let's look at the second inequality $x<-\frac{5}{2}$ This means that x is less than -5/2.