Solving Linear Inequality

What would happen if we added the same positive number to both sides of an inequality? Try adding 3 to each side of the inequalities. Is the resulting inequality true?

What if we added a negative number instead?  Let’s try adding a negative number.  Is the inequality still true?

Note that adding a negative number is the same as subtracting the positive number; therefore, -2 + (-7) = -2 – 7. 

Does the same thing happen with multiplication and division?

Let’s find out.

Try multiplying both sides of the inequalities by the same positive number. Let’s use 4.

What if we multiplied both sides by a negative 4.   Will the inequality statement still be true?

Let’s find out.

What if we divided both sides by a negative 1.   Will the inequality statement still be true?

Let’s find out.