Answer :
One example:
[tex]x<12 \ \ \ |\times 2 \\ 2x<24 \ \ \ |+2x \\ 4x<24+2x \\ \boxed{4x<2(12+x)}[/tex]
Another example:
[tex]x<12 \ \ \ |\div (-2) \\ -\frac{1}{2}x>-6 \ \ \ |+8 \\ \boxed{-\frac{1}{2}x+8>2}[/tex]
[tex]x<12 \ \ \ |\times 2 \\ 2x<24 \ \ \ |+2x \\ 4x<24+2x \\ \boxed{4x<2(12+x)}[/tex]
Another example:
[tex]x<12 \ \ \ |\div (-2) \\ -\frac{1}{2}x>-6 \ \ \ |+8 \\ \boxed{-\frac{1}{2}x+8>2}[/tex]
Here is another example:
X + 8 < 20
You find the solution to that inequality this way:
X + 8 < 20 ---- start with the example
X + 8 - 8 < 20 - 8 ----- subtract 8 from each side
X < 12 ---- gives you the solution you're looking for
Note:
A way to find a different inequality with that solution is to start with that solution:
X < 12
Then, do a mathematical operation to each side, such as "subtract 3":
X - 3 < 12 - 3
Simplify the resulting inequality:
X - 3 < 9
Which gives you an inequality with the solution you're looking for.
X + 8 < 20
You find the solution to that inequality this way:
X + 8 < 20 ---- start with the example
X + 8 - 8 < 20 - 8 ----- subtract 8 from each side
X < 12 ---- gives you the solution you're looking for
Note:
A way to find a different inequality with that solution is to start with that solution:
X < 12
Then, do a mathematical operation to each side, such as "subtract 3":
X - 3 < 12 - 3
Simplify the resulting inequality:
X - 3 < 9
Which gives you an inequality with the solution you're looking for.
