In this Section:
In this section, we continue to learn about solving a very simple type of equation, a linear equation in one variable. We will focus on equations of the form: ax = c. To solve this type of equation, we must learn another two properties. The first is known as the multiplicative inverse property. This property tells us that a number times its reciprocal is one. Another way of thinking about this is a non-zero number divided by itself is always one. The second property is known as the multiplication property of equality. This property tells us that we can multiply or divide both sides of an equation by the same non-zero number and not change the solution. Using these two properties together allows us to solve simple equations such as: 2x = 12. We can divide both sides of the equation by two and isolate x: -> 2x ÷ 2 = 12 ÷ 2 -> x = 6. We see that x in this case is equal to six. We can check by asking does two times six equal twelve? The answer is yes and so the solution x = 6 is correct.