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When rewriting inequalities using subtraction it's important to make the **the same operation on both sides** to ensure that the inequality still holds. So, if one side is subtracted by a number, the other side must be subtracted by the same number. In the inequality $8x+3=19$ both sides can be subtracted by $3.$
$8x+3\,{\color{#FF0000}{-\,3}}<19\,{\color{#FF0000}{-\,3}} \quad \Leftrightarrow \quad 8x<16$