Question

Select all expressions that are equivalent to

0.75x + 0.25(x + 12.4) + (x – 2.1)
A. 2x + 1
B. x + 1
C. x + 3.1 + x + 2.1
D. x + 3.1 + x – 2.1


Please tell me what to do. I am in need of help. Thank you!!

Answer 1

Answer: Both A.) 2x + 1 and D.) x + 3.1 + x – 2.1

The question says select all equivalent expressions

Step-by-step explanation:

0.75x + 0.25(x + 12.4) + (x – 2.1)

distribute 0.25 in the middle term 0.25 × 12.4 = 3.1

and "multiply by +1" the second parentheses to remove them

0.75x + 0.25x + 3.1 + x – 2.1

add the decimal coefficients 0.75x + 0.25x = 1.00x (means 1x) so: = x

x + 3.1 + x - 2.1 This is choice D an equivalent expression

simplify by combining like terms to get

2x + 1 This is choice A

Answer 2

The answer is A
Explanation:
1. first distribute 0.25 into (x+12.4) which is 0.25+3.1
2. New slightly simpler equation is 0.75x+0.25x+3.1+x-2.1
3. Add similar terms
-0.75x+0.25x+x=2x
-3.1-2.1= 1
4. Simplified is 2x+1