Which expression is equivalent to 2.8k – 8.4? A. 0.07(4k – 12) B. 0.7(4k – 12) C. 5.6k D. -5.6k
Which expression is equivalent to 2.8k – 8.4? A. 0.07(4k – 12) B. 0.7(4k – 12) C. 5.6k D. -5.6k
The Correct Answer and Explanation is:
The correct answer is: B. 0.7(4k – 12)
Explanation:
We are given the expression: 2.8k−8.42.8k – 8.4
We are asked to find an equivalent expression from the options provided. To do this, we can factor the expression or distribute the expressions in the options to see which one matches.
Step 1: Factor the original expression
Let’s factor out the greatest common factor from both terms in the expression: 2.8k−8.42.8k – 8.4
We can factor out 0.7, since:
- 2.8÷0.7=42.8 \div 0.7 = 4
- 8.4÷0.7=128.4 \div 0.7 = 12
So: 2.8k−8.4=0.7(4k−12)2.8k – 8.4 = 0.7(4k – 12)
This matches option B.
Step 2: Distribute Option B to check
Let’s check the distribution of B. 0.7(4k – 12): 0.7⋅4k=2.8k0.7⋅(−12)=−8.40.7 \cdot 4k = 2.8k\\ 0.7 \cdot (-12) = -8.4
So: 0.7(4k−12)=2.8k−8.40.7(4k – 12) = 2.8k – 8.4
That confirms that option B is equivalent to the original expression.
Why the other options are incorrect:
- Option A: 0.07(4k – 12) 0.07⋅4k=0.28k,0.07⋅(−12)=−0.840.07 \cdot 4k = 0.28k, \quad 0.07 \cdot (-12) = -0.84 This gives 0.28k−0.840.28k – 0.84, which is not equal to 2.8k−8.42.8k – 8.4.
- Option C: 5.6k
This is a single term and cannot represent the full two-term expression. - Option D: -5.6k
Also just one term, and not equivalent to the original expression.
Conclusion:
By factoring and distributing, we verify that option B (0.7(4k – 12)) is equivalent to the expression 2.8k−8.42.8k – 8.4. The process of factoring helps to identify common patterns and simplify expressions, which is a valuable algebraic skill.
