Question

1. consider the following statement: 3 > -3

15a add 4 to both sides of the inequality and simplify.
3 + 4 > -3 + 4
explain

Explanation:

Step1: Recall inequality property

When adding a number to both sides of an inequality, the direction of the inequality sign remains the same. The property is: if \(a > b\), then \(a + c>b + c\) for any real number \(c\).
Here, \(a = 3\), \(b=- 3\) and \(c = 4\). So we add 4 to both sides of \(3>-3\), getting \(3 + 4>-3 + 4\).

Step2: Simplify both sides

Calculate \(3+4 = 7\) and \(-3 + 4=1\). So the inequality becomes \(7>1\), which is a true statement.

Answer:

When we add 4 to both sides of \(3>-3\) (using the property of inequalities that adding a number to both sides preserves the inequality direction), we get \(3 + 4>-3 + 4\). Simplifying, \(7>1\), which is true. So the step \(3 + 4>-3 + 4\) is valid as it follows the inequality addition property and the simplified result is a true inequality.