Does the inequality sign change when adding or subtracting? This is a common question that arises when working with inequalities in mathematics. The answer to this question is both yes and no, depending on the circumstances. Let me explain further.
Rule 1 states that adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged. In other words, if we have an inequality such as “a < b" and we add or subtract the same quantity from both sides, the inequality sign remains the same. For example, if we add 3 to both sides of the inequality, we have "a + 3 < b + 3", and the inequality sign remains unchanged.
To illustrate this rule, let me provide a personal experience. When I was studying algebra in high school, we often encountered inequalities in our math problems. I vividly remember a particular problem where we had to solve the inequality "2x - 5 > 9″. To isolate the variable, we added 5 to both sides of the inequality, resulting in “2x > 14”. As we added the same quantity to both sides, the inequality sign remained unchanged.On the other hand, Rule 2 states that multiplying or dividing both sides of an inequality by a positive number also leaves the inequality symbol unchanged. This means that if we have an inequality like “c > d” and we multiply or divide both sides by a positive number, the inequality sign remains the same. For instance, if we multiply both sides by 2, we get “2c > 2d”, and the inequality sign remains unchanged.
To provide a real-life example, let’s consider a situation where you have a certain amount of money and want to save more. You decide to increase your savings each month by multiplying it by a factor of 1.5. If your original savings were represented by the inequality “x > 100”, multiplying both sides by 1.5 gives you “1.5x > 150”. The inequality sign remains the same since we multiplied by a positive number.
It’s important to note that these rules only hold true when we add or subtract the same quantity or multiply or divide by a positive number. If we were to add or subtract different quantities or multiply or divide by a negative number, the inequality sign would change.
The inequality sign does not change when adding or subtracting the same quantity from both sides or when multiplying or dividing both sides by a positive number. These rules are essential in solving inequalities and understanding their properties. By applying these rules correctly, we can manipulate inequalities to find solutions and make mathematical reasoning more manageable.