Question

How do you solve 5x < 2x – 6?

Answer 1

Hint: We have inequality given in the question and have to solve for the possible values of x. So, we will try to transpose and rearrange the terms such that we get x on one side of the inequality and constants on the other side. So, we will start by shifting 2x from RHS to LHS and then simplify further to get the answer.

Complete step by step answer:
We have been provided with an inequality 5x < 2x – 6 in the question. Since it is not a linear equation, we can have many values of x. By solving it, we will be able to find the possible values of x. In order to solve it, we will first transpose the term 2x to the RHS. Since we are transposing to the other side of the inequality, the sign of the term will change. So, 2x will become -2x. So, we will get
5x – 2x < – 6
Now, we can simplify 5x and 2x by subtracting them to obtain 3x. This will leave us with simplified inequality as below,
3x < -6
Since we require the value of x, we have to make 3x to x. To do that, we will divide both sides of the inequality by 3. Doing so, we will get
$\dfrac{3x}{3}<\dfrac{-6}{3}$
Since we know that $\dfrac{3}{3}=1$ and $\dfrac{-6}{3}=-2$ , we can rewrite the inequality as
x < -2

We have hence reached our final answer and x can have all values less than -2.

Note: In this question, we have followed the approach of simplifying the given inequality to obtain the values of x. We can also try to substitute random values of x and get a rough idea of possible values of x. Although this method is not recommended for easy level questions since it will simply lead to wastage of time. If we were to use this method, we could have started with x = -3 to obtain -15 < -6-6, which is possible.