Question

How do you solve the inequality \[x - 1 > 2\]?

Answer 1

Hint: 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.