4 Using an Equation with Variables on Both sides It takes a graphic designer 1.5 h to make one page of a website. With new software, he could complete a page in 1.25 h, but it takes 8 h to learn. How many pages would he have to make in order to save time using the new software?What do we know?What are we looking for?Make an equation1.5p = 1.25p + 8p= 32 means with 32 pages the time is the same
5 Solving Using the Distributive Property Distribute first, then solve.Examples:2(5x – 1) = 3(x + 11)4(2y + 1) = 2(y – 13)
6 IdentitiesAn equation that is true for every possible value of the variable is an identity.This can happen when variables cancel and you are left with a true statement.Ex: x + 1 = x + 1After moving variables to one side, you are left with 1 = 1, which is true.
7 Equations with No Solution When variables cancel and you are left with a false statement, the equation has no solution.Ex: x + 2 = x – 4After moving variables to one side, you are left with 2 = -4, which is false.
8 Practice Tell whether the equation is an identity or has no solution. 10x +12 = 2(5x + 6)9m – 4 = -3m m3y – 5 = 3(-2 + y)