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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

Absolute Value Equations

The absolute value of a number x is the distance from x to 0 on the real number line and is written as |x|. The absolute value function can be written as a "piecewise-defined function". Therefore, when solving absolute value equations, you need to consider 2 cases. The first case considers what happens when x is positive and the second is when x is negative. 

|x|= x if x 0

|x|= - x if x < 0

Solving Equations and Inequalities

When solving equations or inequalities that involve absolute value, the following three principles will be useful. Notice that you will be required to solve two separate parts corresponding to two different cases. The first step is to separate the equation or inequality into it's two cases and remove the absolute value signs. The second step is to solve the equations or inequalities as usual.

If a > 0, then

  • |x| = a if and only if x = ± a;
  • |x| < a if and only if - a < x < a; and
  • |x| > a if and only if x > a or x < -a.

solving equations and inequalities

Example: Solve |x + 5| < 1 for x.


-1 < x + 5 < 1

-1 < x + 5                           x + 5 < 1

-6 < x                                        x < -4

Therefore, -6 < x < -4.