Question

Solve the inequality$\frac{1}{4}x-\frac{1}{12}x>\frac{1}{6}x+\frac{7}{8}$, graph the solution on the number line, and write the solution in interval notation .

Short answer

There is no solution of the inequality $\frac{1}{4}x-\frac{1}{12}>\frac{1}{6}x+\frac{7}{8}$

The graph of the solution is :-

Step-by-step solution

Step 1. Given information

We have given the following inequality :-

$\frac{1}{4}x-\frac{1}{12}x>\frac{1}{6}x+\frac{7}{8}$.

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.

Step 2. Solving the inequality

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

$$\begin{gathered} 24(\frac{1}{4}x-\frac{1}{12}x)>24(\frac{1}{6}x+\frac{7}{8}) \\ \Rightarrow 6x-2x>4x+21 \\ \Rightarrow 4x>4x+21 \end{gathered}$$

Subtract $4x$from both sides, then we have :-

$$\begin{gathered} 4x-4x>4x+21-4x \\ \Rightarrow 0>21 \end{gathered}$$

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 :-