Question

How do you solve \[2x-1<9\]?

Answer 1

Hint: This type of problem is based on the concept of inequality. First, we have to consider the whole function. Then, we need to add the whole equation with 1. And do some necessary calculations. And then, divide the whole equation by 2 so that we get x in the left-hand side of the inequality. Solve x considering the inequality.

Complete step by step solution:
According to the question, we are asked to solve the inequality \[2x-1<9\].
We have been given the inequality is \[2x-1<9\]. -----(1)
We first have to add the whole inequality by 1.
\[\Rightarrow 2x-1+1<9+1\]
We know that terms with the same magnitude and opposite signs cancel out. On cancelling 1, we get
\[2x<9+1\]
On further simplification, we get
\[2x<10\]
We can express the inequality as
\[2x<2\times 5\]
We find that 2 are common in both the sides of the inequality.
To cancel 2, we have to divide the obtained inequality by 2.
\[\Rightarrow \dfrac{2x}{2}<\dfrac{2\times 5}{2}\]
We find that 2 are common in both the numerator and denominator of LHS and RHS of the inequality. Cancelling 2, we get
\[x<5\]
We can also write the value of x as \[\left( -\infty ,5 \right)\].

Therefore, the value of x in the given inequality \[2x-1<9\] is \[x<5\], that is \[x\in \left( -\infty ,5 \right)\].

Note: Whenever you get this type of problem, we should always try to make the necessary changes in the given inequality to get the final solution of the equation which will be the required answer. We should always make some necessary calculations to obtain x in the left-hand side of the equation. We should avoid calculation mistakes based on sign conventions. We should not write the value of x in a closed bracket, that is \[\left[ -\infty ,5 \right]\]. This is completely wrong. Close bracket is mentioned only when 5 is also included in the value of x.