An inequality shows a relationship between two or more expressions (or terms) that is not equal. There are numerical inequalities and algebraic inequalities. Numerical inequalities use only numbers while algebraic inequalities use variables to compare. The solution set shows the answers that make the inequality true when it is solved and/or graphed. Inequalities can have one of five different signs. See the image below for how to graph each of the signs, how to write the inequality (both ways using the symmetric property), and key words that represent that particular sign
When you have a variable in an inequality, the variable represents all the numbers that are possible answers, called the solution set. These answers are being compared to the other number in the inequality. For example in x < 1, the solution set is any number less than 1 but not 1 or any number higher. Therefore if we needed to find possible solutions for x < 1, we would say any number lower than 1 is a solution. This is important to remember for solving inequalities in the next journal entry.
The difference between "is less than", "less than" and "less".
Notice that in inequality word problems, the word "is" (or some variation of it like has or was) is present. However, sometimes we can confuse it with the meaning for "less than" or "less". Remember that is means = sign, but if something IS less than then it is not equal.
If, instead you see, 5 less than 10, that means to subtract because the word IS isn't there. So the expression would be 10-5 for 5 less than 10. The word than makes us reverse the order of the term being subtracted.
Lastly, 5 less 10 still means to subtract, but the expression would be 5 - 10.
The worksheet below was used during class to provide practice problems on writing and graphing inequalities.