Why does the inequality sign change when both sides are
multiplied or divided by a negative number? Does this happen with equations? Why or why not?
Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.
http://www.purplemath.com/modules/ineqsolv.htm
The inequality sign changes when both sides are multiplied or divided by a negative number because multiplying or dividing by a negative number flips the direction of the inequality. This happens because negative numbers are considered to be "less than" positive numbers.
To understand why this happens, let's consider an example with a simple inequality:
3 < 5
If we multiply both sides of this inequality by -1, we get:
-3 > -5
The inequality sign changes from "less than" (<) to "greater than" (>). This is because -3 is greater than -5.
However, this does not happen with equations. When dealing with equations, adding, subtracting, multiplying, or dividing by the same number on both sides will not change the equality because both sides of the equation are being operated on equally. The operations maintain the equality of the equation.
Now, let's create an inequality for your classmates to solve using both the multiplication and addition properties:
2x + 5 > 10
In this inequality, we can utilize both the multiplication and addition properties. To solve it, we need to isolate the variable x on one side of the inequality.
First, subtract 5 from both sides:
2x > 10 - 5
2x > 5
Next, divide both sides by 2:
x > 5/2
So the solution to the inequality is x > 2.5.