Question

How do you solve the inequality $x - 1 > 2$?

Answer 1

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Here we need to solve for ‘x’ which is a variable. Solving the given inequality is very like solving equations and we do most of the same thing but we must pay attention to the direction of inequality$( \leqslant , > )$. We have a simple linear equation type inequality and we can solve this easily.

Complete step by step solution:
Given $x - 1 > 2$
We need to solve for ‘x’.
Since we know that the direction of inequality doesn’t change if we add a number on both sides. We add 1 on both sides of the inequality we have,
$x - 1 + 1 > 2 + 1$
$x > 3$
That is $x > 3$ is the solution of $x - 1 > 2$.
We can write it in the interval form. That is $(3,\infty )$

Note: If we take a value of ‘x’ in $(3,\infty )$ and put it in $x - 1 > 2$, it satisfies. That is
Let put $x = 4$ in $x - 1 > 2$,
$4 - 1 > 2$
$3 > 2$
That is 3 is greater than 2 and it is correct.
We know that $a \ne b$says that ‘a’ is not equal to ‘b’. $a > b$ means that ‘a’ is less than ‘b’. $a < b$ means that ‘a’ is greater than ‘b’. These two are known as strict inequality. $a \geqslant b$ means that ‘a’ is less than or equal to ‘b’. $a \leqslant b$ means that ‘a’ is greater than or equal to ‘b’.

The direction of inequality do not change in these cases:
i) Add or subtract a number from both sides.
ii) Multiply or divide both sides by a positive number.
iii) Simplify a side.

The direction of the inequality change in these cases:
i) Multiply or divide both sides by a negative number.
ii) Swapping left and right hand sides.