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How to Solve Inequalities with Fractions?

TopIn algebra, if we want to solve any inequality, then we have to check that given condition is true or not. For that, we put the random values in variable terms. The inequality term is basically written with following symbols <, >, $\leq$, $\geq$.

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

  1. 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.
  2. If any term in the inequality is in fraction form, then we multiply the whole term (both hand sides) by denominator.
  3. After that, we solve the inequality according to the operator or divide the constant term by variable co - efficient to isolate the variable.
  4. 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.