Final answer:
When solving equations, the properties of equality state that adding or subtracting the same quantity from both sides will not change the result. Inequalities have similar properties, but if we add or subtract a negative quantity, the inequality sign is reversed. Multiplying or dividing by a negative number also requires reversing the inequality sign.
Step-by-step explanation:
When solving equations, the properties of equality state that if the same quantity is added to or subtracted from both sides of the equation, the result will still be true. The properties of inequality, however, are slightly different. If the same positive quantity is added to or subtracted from both sides of an inequality, the inequality sign remains the same. But if the same negative quantity is added to or subtracted from both sides, the inequality sign is reversed.
For example, if we have the equation 4x + 5 = 13, we can subtract 5 from both sides to find that 4x = 8. This follows the properties of equality. However, if we have the inequality 2x - 3 < 7, we can add 3 to both sides to get 2x < 10. In this case, the inequality sign remains the same because we added a positive quantity.
Another important property of inequality is that when multiplying or dividing both sides by a negative number, the inequality sign must be reversed. For example, if we have the inequality -2x > 10, dividing both sides by -2 gives us x < -5. The inequality sign is reversed because we divided by a negative number.
Learn more about properties of equality and inequality