Question

How do you solve $6x - 6 > - 12$?

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 $6x - 6 > - 12$
Since we know that the direction of inequality doesn’t change if we add or subtract a number on both sides. We add ‘6’ on both sides of the inequality we have,
$\Rightarrow 6x > - 12 + 6$
$\Rightarrow 6x > - 6$
We divide the whole inequality by 6 we have,
$\Rightarrow x > \dfrac{{ - 6}}{6}$
$\Rightarrow x > - 1$
Thus the solution of $6x - 6 > - 12$ is $x > - 1$.
We can write it in the interval form. That is $( - 1,\infty )$.

Note: If we take a value of ‘w’ in $( - 1,\infty )$ and put it in $6x - 6 > - 12$, it satisfies. That is
Let put $x = 1$ in $6x - 6 > - 12$,
$6(1) - 6 > - 12$
$6 - 6 > - 12$
$0 > - 12$, which is true. Hence the obtained solution is correct.
We know that $a \ne b$is 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:
- Add or subtract a number from both sides.
- Multiply or divide both sides by a positive number.
- Simplify a side.
- The direction of the inequality change in these cases:
- Multiply or divide both sides by a negative number.
- Swapping left and right hand sides.