Question

Solve the inequation \[2x + 6 < 12\]?

Answer 1

Hint: Here we have an inequality equation. 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 \[2x + 6 < 12\]
We need to solve for ‘x’
Since we know that the direction of inequality doesn’t change if we subtract a number on both sides. We subtract 6 on both sides of the inequality we have,
\[2x + 6 - 6 < 12 - 6\]
\[\Rightarrow 2x < 6\]
We divide the whole equation by 2 which is positive so here we don’t have the direction change of the inequality sign as,
\[x < \dfrac{6}{2}\]
\[ \Rightarrow x < 3\]
That is \[ \Rightarrow x < 3\] is the solution of \[2x + 6 < 12\].

Note: We know that \[a \ne b\]it 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 does not change in these cases:
\[ \bullet \] Add or subtract a number from both sides.
\[ \bullet \] Multiply or divide both sides by a positive number.
\[ \bullet \] Simplify a side.
The direction of the inequality change in these cases:
\[ \bullet \] Multiply or divide both sides by a negative number.
\[ \bullet \] Swapping left and right-hand sides.