Question

For each expression, select all equivalent expressions from the list.(a) 2x+1402.X+272(x+7)2(7x+1)16x(b) 16 +12y-6-y11 +10y10y+1110y +11 y11 y +10

Answer 1

We must find equivalent expressions by performing some algebraic operations

Let's start with the first expression:

(a) 2x+14

Please note that both 2x and 14 are divisible by 2.

Take 2 as a common factor like this:

2x+14 = 2(x+7)

Note that if we multiply 2(x+7) we get 2x+14

Thus, the expression is equivalent to 2(x+7)

Now for the following expression:

(b) 16 + 12y - 6 - y

We can note there are numbers apart from variables. The numbers that appear without any variable, can be joined. The variables with the same letter can also be joined:

16 - 6 = 10

12y - y = 11y

Thus, the equivalent expression is

11y+10