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Chapter 2: Q 2.110 (page 177)

Solve the inequality 25z-13z<115z-35, graph the solution on the number line, and write the solution in interval notation.

Short Answer

Expert verified

There is no solution of the given inequality25z-13z<115z-35.

Step by step solution

01

Step 1. Given information

We have given the following inequality :-

25z-13z<115z-35.

We have to solve the inequality for values of x.

We will be apply some arithmetic operations, that will convert the quality to a inequality from which we easily determine the interval of solution.

02

z-z<z-z-9⇒0<-9Step 2. Solve the inequality

Multiply both sides with LCD 15, to clear the fractions, then we have :-

15(25z-13z)<15(115z-35)鈬�6z-5z<z-9鈬�z<z-9

Now subtract zfrom both sides, then we have :-

z-z<z-z-9鈬�0<-9

This is a contraction.

03

Step 3. Conclusion

As there is a contraction while solving the inequality.

So that the given inequality is not true.

Hence we can conclude that the given inequality hasno solution.

We can draw the solution graph as following :-

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