Solving Inequalities Basics

Solving Inequalities

By MARIA FAROOQI

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On a scale of 1-5 (1=terrible, 5=fantastic) how do you feel today?

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Open Ended

I feel ______ this morning

Inequality 😏

An inequality is a comparison that relates two values.

Here are some examples ​of inequalities:

9x ​- 5 ≤ 50

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12 <​ 85

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Inequalities| Algebra 1

​The table below shows symbols you might see in an inequality.

​If your inequality has a variable , you can solve it by getting the variable alone. The solution to an inequality tells you the values of the variable that make the inequality true.

​For example, think about the inequality

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What can "p" be?​

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​The solution to this inequality is p > 3. In other words, the inequality is true if p is any value greater than 3. You can plug in some values to check your work.

If p is 7, you get 7+1 > 4, or 8 > 4, which is true.😁

If p is 2, you get 2+1 > 4, or 3 > 4, which is not true.😩

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Remember, our solution tells us that p must be greater than 3. 😧

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Solving inequalities with variables is similar to solving equations. You can often find the solution to a one-variable inequality by getting the variable alone on one side of the inequality. You can use inverse operations to help.

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​But be careful!

There are two situations in which you'll need to change the direction of your inequality sign.

1. If you swap the right and left sides of the inequality, you must flip the inequality sign. For example, x ≥ 7 would become 7 ≤ x.

2. If you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

   For example, when you divide by – 2,

   – 2x > – 4 becomes x < 2.

Poll

Let's try it! Solve $$-4t\le-20$$  . The solution is...

• $$t<5$$  

• $$t\le5$$  

• $$t>5$$  

• $$t\ge5$$  

​Divide or multiply both sides of an inequality by a negative number, FLIP THE INEQUALITY SIGN.

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