Question

How do you solve \[6x - 6 > - 12\]?

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 \[6x - 6 > - 12\]
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.