If we want to know how to solve inequalities with fractions, then we have to follow some steps which are as follows:

- We first, move all variable terms in left hand side and all constant terms in right hand side and while moving terms, it is necessary that sign should be changed.
- If any term in the inequality is in fraction form, then we multiply the whole term (both hand sides) by denominator.
- After that, we solve the inequality according to the operator or divide the constant term by variable co - efficient to isolate the variable.
- Next, we put the random values of variable and check that inequality satisfies for given value or not.

To understand fraction inequalities, we take an example of inequality ($\frac{-2}{3}$) k + 6 $\leq$ 1.

Here, we can easily see that the denominator is 3 in the first term of the left hand side. So, we multiply the whole inequality with 3.

-2k + 18 $\leq$ 3,

Now, we move all the constant terms on the right hand side and all the variable terms on the left hand side. So, after moving, we get

-2x $\leq$ 3 - 18,

Now, we subtract 18 from both side by adding -18.

-2x $\leq$ -15,

To remove the negative sign, we divide -15 with the co-efficient of variable ‘x’ which is -2 and change the direction of an inequality.

So, x ≥ $\frac{15}{2}$.

Here, the variable ‘x’ is greater than or equals to value $\frac{15}{2}$.

Use the below widget to simplify rational inequalities.

Use the below widget to simplify rational inequalities.