Solving Inequalities using a Number Line

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line.

Matching inequalities, Number sets and Number Lines

Solving Inequalities

At the start of the lesson students recap matching an inequality to its corresponding list of integer values and number line which we learned last lesson.  To ensure no time is wasted copying from the board I provide an A5 handout of this slide for students as they enter the classroom.  When ready, I feedback the matching representations to ensure all can proceed with the main part of the lesson.

Solving inequalities using a number line

To aid the process of solving an inequality it is important to provide a clear writing frame to show how the inequality remains balanced as it is simplified.  Students are familiar with the balance method from solving two-step equations.

After working through a couple of examples with the class I ask them to show me the solutions to the inequality 3x – 4 > 17 on a number line.  Nearly all the students apply the balance method correctly to arrive at x > 7.  However, about a quarter of the class forget to show this on a number line as this is not a step required when solving equations.  After feeding back we attempt a similar question which all students complete correctly.

Inequalities between two points

After a bit more practice we move onto inequalities that are bounded between two numbers.  I ask the students to split –10 < 2x ≤ 16 into two separate inequalities.  Without any prompting from me all the students separate it into  –10 < 2x and 2x ≤ 16.  I now ask the class to solve the two inequalities and represent their solutions on a single number line.

All the class could solve –10 < 2x as –5 < x.  However, the most common representation on a number line was x < -5.

Solving Inequalities

We discuss if –5 is less than x then x must be greater than –5.  When understood in this way all students could show this correctly on the number line.

Solving Inequalities

After a couple more questions it is clear the class are ready to work independently through the questions on the third slide and later, the differentiated worksheet.  This takes up about 25 to 30 minutes of the lesson. 

Assessing Progress and Feeding Back

The plenary is printed on the reverse side of the A5 sheet they were given at the start of the lesson.  This typically takes 10 minutes to complete and I encourage students to complete the work in their book.  To feedback and check progress I ask students to show me their completed A5 sheet at the end of the lesson.

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