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Question

Question: How do you solve \(5x < \- 4\) ?...

How do you solve 5x<\-45x < \- 4 ?

Explanation

Solution

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<\-45x < \- 4.

To solve an inequality in one variable, we first try to isolate the variable from it.
Here the variable is xx.
The coefficient of xx is 55.

So, to isolate the variable xx which is multiplied by 55 we simply divide the whole inequality by that coefficient i.e., 55

Dividing both the sides of the inequality by 55,
5x5<45\Rightarrow \dfrac{{5x}}{5} < \dfrac{{ - 4}}{5}
On simplifying this, we get,
x<45\Rightarrow x < \dfrac{{ - 4}}{5}
Therefore, we get the value of x<45x < \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.