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Chapter 2: Q 2.109 (page 177)

Solve the inequality14x-112x>16x+78, graph the solution on the number line, and write the solution in interval notation .

Short Answer

Expert verified

There is no solution of the inequality 14x-112>16x+78

The graph of the solution is :-

Step by step solution

01

Step 1. Given information

We have given the following inequality :-

14x-112x>16x+78.

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

Step 2. Solving the inequality

Multiply both sides of inequality by LCD 24, to clear the fraction. Then we have :-

24(14x-112x)>24(16x+78)鈬�6x-2x>4x+21鈬�4x>4x+21

Subtract 4xfrom both sides, then we have :-

4x-4x>4x+21-4x鈬�0>21

03

Step 3. Final Conclusion

As we find 0>21.

This is a contraction.

So that we can conclude that given inequality has no solution.

The solution graph is as following :-

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