Question

Understanding How to Simplify Expressions
Consider the expression
2
3
(14x − 3) − 3x(
4
5
+ 5).

Which statements are true about simplifying this expression? Check all that apply.

Using the distributive property, the Two-thirds would be multiplied to 14x and to –3.
Combining Four-fifths + 5 can be done before multiplying it by 3x.
Using the distributive property, 3x times Four-fifths is subtracted, but the 3x times 5 is added.
Combining 14x – 3 can be done before multiplying by Two-thirds.
Subtracting 3x is the same as adding –3x.

Answer 1

True:
- Using the distributive property, the Two-thirds would be multiplied to 14x and to –3. (2/3*(14x−3) = (2/3)*14x + (2/3)*(−3).)
- Combining Four-fifths + 5 can be done before multiplying it by 3x. (4/5 + 5 = 29/5, then multiply by 3x.)
- Subtracting 3x is the same as adding –3x. (−3x = + (−3x).)

False:
- Using the distributive property, 3x times Four-fifths is subtracted, but the 3x times 5 is added. (Both terms are subtracted: −3x(4/5+5) = −3x*(4/5) − 3x*5.)
- Combining 14x − 3 can be done before multiplying by Two-thirds. (14x and −3 are unlike terms and cannot be combined.)