Simplify the expression: Use the distributive property to remove parentheses first: 2(3s 1) – 7(s 11) 2(3s 1) – 7(s 11) = (Simplify your answer:)
The Correct Answer and Explanation is:
Simplified Expression:
Given:2(3s+1)−7(s+11)2(3s + 1) – 7(s + 11)2(3s+1)−7(s+11)
Step 1: Apply the distributive property to each term.
Distribute the 2 across (3s + 1):2⋅3s=6s,2⋅1=22 \cdot 3s = 6s,\quad 2 \cdot 1 = 22⋅3s=6s,2⋅1=2
So,2(3s+1)=6s+22(3s + 1) = 6s + 22(3s+1)=6s+2
Distribute the -7 across (s + 11):−7⋅s=−7s,−7⋅11=−77-7 \cdot s = -7s,\quad -7 \cdot 11 = -77−7⋅s=−7s,−7⋅11=−77
So,−7(s+11)=−7s−77-7(s + 11) = -7s – 77−7(s+11)=−7s−77
Step 2: Combine all parts.6s+2−7s−776s + 2 – 7s – 776s+2−7s−77
Step 3: Combine like terms.
- Combine 6s – 7s = -s
- Combine 2 – 77 = -75
Final Answer:−s−75-s – 75−s−75
Explanation
To simplify expressions involving parentheses, the distributive property plays a key role. This property states that a number multiplied by a sum (or difference) inside parentheses must be distributed to each term within the parentheses. Begin by identifying the two sets of parentheses: 2(3s + 1) and -7(s + 11).
The first part, 2(3s + 1), involves multiplying 2 by both 3s and 1. Multiplying 2 by 3s results in 6s, and 2 by 1 gives 2. So, the expression becomes 6s + 2.
Next, look at the second part, -7(s + 11). Here, the -7 must be distributed to both s and 11. Multiply -7 by s to get -7s, and -7 by 11 to get -77. This results in -7s – 77.
Now, substitute these new expressions back into the original expression:
6s + 2 – 7s – 77
To simplify, combine like terms. First, group the terms with the variable s. Combine 6s and -7s, which gives -s. Then, group the constant terms 2 and -77; combining these gives -75.
Putting the simplified terms together results in the final simplified expression:
-s – 75
This expression no longer contains parentheses, and all like terms have been combined correctly, giving a fully simplified form.
