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This is the kind of thing to which I think you are referring.

You have an equation such as 4x + 5 = 2x + 3.

You can subtract 2x from both sides to obtain, 2x + 5 = 3,

then add -5 to both sides to obtain 2x = -2,

then divide both sides by 2 to obtain x = -1.

You can do very much the same thing with an inequality such as 4x + 5 lt 2x + 3.

The same steps yield x lt -1.

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Q: How can you use the addition and subtraction properties of equality to produce equivalent inequalities?
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