Solving Linear Inequality

LEARNING INTENTION

We are learning how to solve linear inequalities to solve

mathematical and real-world problems.

SUCCESS CRITERIA

I can solve linear inequalities with variables on both sides.

• I can simplify an expression using the distributive

property.

PRIOR KNOWLEDGE REVIEW

-2 < 5

6 > 4

-3 < -1

2 > -8

In middle school, you learned that you could use a number line to compare numbers. The inequalities statements shown are true.

Open Ended

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?

Open Ended

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. 

Open Ended

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.

Open Ended

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

Let’s find out.

Open Ended

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

Let’s find out.

SUMMARY

When you add or subtract the same number to both sides of an

inequality, the order of the inequality remains the same.

HOWEVER

When you multiply or divide both sides of an inequality by a negative
number the order of the inequality REVERSES to make the statement

true.

Inequality

Video