Solving an equation with one unknown From arithmetic to algebra Modifying equations in algebra

Solving an equation with one unknown Today, we will use the rules of arithmetic seen last week to solve an equation with one unknown As for last week, the exercises for next week are intended to get you used to solving equations Again, the slides provide list of properties you can go back to for reference

Solving an equation with one unknown From arithmetic to algebra Solving equations

From arithmetic to algebra Last week we saw the rules for using addition, subtraction, multiplication and division to perform calculations Like the examples we’ve seen… Today we examine how you can use the same rules and notation to solve equations What’s the difference ?

From arithmetic to algebra An equation is a line of calculation that contains an “=” sign: An equation can contain unknown “x, y, z” the value of which is not given The numbers that are known are called parameters

From arithmetic to algebra With the calculations, the aim was to find the following result (for example): In fact, a calculation is simply an equation where the unknown is isolated on one side of the equation !!

From arithmetic to algebra When an equation contains an unknown “x” the aim is to find the value(s) of “x” for which the equation is true In other words, “solving an equation” means finding the value of the unknown for which the equality holds Example : is the equation true if x=10? What if x=-20?

From arithmetic to algebra In the general case, the unknown is not isolated, like in a calculation: Therefore, the aim is to modify the equation until you can isolate the unknown: At that point, what you have is a calculation you can solve

From arithmetic to algebra The rules in the following section also apply to the case where the parameters of the equation (the numbers) are also unknown However, you can use the same method to isolate the unknown It is simply the final calculation that you can’t perform. You have some examples in the exercises

Solving an equation with one unknown From arithmetic to algebra Solving equations

Lets try and solve the following equation In other words find the value of x such that the equation is true. The goal is to isolate “x” on one side. How do you do it? Use the rules from last week. Identify the grouped operations Move the groups until you have isolated x Important: take all the steps you need to do so !

Solving equations When modifying the equation take advantage of the fact that carrying out an operation on both sides of an equation does not change the equation Step 1: move “2” to the other side

Solving equations Step 2: if you want, you can carry out some calculations at the same time Step 3: Move ×3 to the other side by dividing both sides by 3:

Solving equations Step 4: Move -6 to the other side by adding 6 on both sides Step 5: Perform the final calculation: Step 6: ALWAYS check by replacing x in the original equation to see if it is true!!