Exercise 110 Page 506

Practice makes perfect

a Before we begin, let's call the given equation 4(3x-1)+3x = 9x+5 a basic equation. To decide which equations are equivalent to the basic equation, we will distribute 4 on the left-hand side to simplify it first.

4(3x-1)+3x=9x+5 ⇕ 12x-4+3x=9x+5 We can see that the simplified form of the basic equation is exactly the same as the given equation from this part. Therefore, they are equivalent.

b Let's compare the given equation to the simplified form of the basic equation that we found in Part A.

Basic equation	Given equation
12x- 4+3x=9x+5	12x- 1+3x=9x+5

We can see that the above equations are the same except one different term. This term cannot be rewritten in a way that the equations will be the same. Thus, the equations are not equivalent.

c Let's compare the given equation to the simplified form of the basic equation that we found in Part A.

Basic equation	Given equation
12x-4+3x=9x+5	11x=14x

Notice that there are significant differences. There are no constant terms in the given equation, while in the simplified form of the basic equation there are constants, which cannot be reduced. Thus, the equations are not equivalent.

d Let's compare the given equation to the simplified form of the basic equation that we found in Part A.

Basic equation	Given equation
12x-4+ 3x=9x+5	15x-4=9x+5

Notice that there are still some differences. Fortunately, in the simplified form of the basic equation we have like terms. Thus, we can combine them. 12x-4+ 3x=9x+5 ⇕ 15x-4=9x+5 We can see that now the simplified form of the basic equation is the same as the given equation from this part. Therefore, they are equivalent.