Question

How do you solve $5x < - 4$ ?

Answer 1

Hint: The given expression is an inequality in one variable. An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. To solve an inequality, we try to isolate the variable from it and simplify further.

Complete step-by-step answer:
The given inequality in one variable is $5x < - 4$.

To solve an inequality in one variable, we first try to isolate the variable from it.
Here the variable is $x$.
The coefficient of $x$ is $5$.

So, to isolate the variable $x$ which is multiplied by $5$ we simply divide the whole inequality by that coefficient i.e., $5$

Dividing both the sides of the inequality by $5$,
$ \Rightarrow \dfrac{{5x}}{5} < \dfrac{{ - 4}}{5}$
On simplifying this, we get,
$ \Rightarrow x < \dfrac{{ - 4}}{5}$
Therefore, we get the value of $x < \dfrac{{ - 4}}{5}$ .

Note: In this problem the coefficient of the variable is positive so there was no change in the sign of inequality but if the coefficient is negative and if we do the division operation , the inequality sign changes. If the sign is ‘greater than’ before dividing by a negative number then it would change to ‘lesser than’ after dividing by a negative number.