Which expression is equivalent to 5(−2.3b − 4.1) − (7b + 0.7)?
−18.5b − 21.2
18.5b − 21.2
−18.5b − 3.4
18.5b + 3.4
The expression 5(−2.3b − 4.1) − (7b + 0.7) can be simplified as follows:
= 5(-2.3b) - 5(4.1) - (7b) - (-0.7)
= -11.5b - 20.5 - 7b - (-0.7)
= -11.5b - 7b - 20.5 + 0.7
= -18.5b - 19.8
Therefore, the correct answer is −18.5b − 19.8.
To find the expression that is equivalent to 5(-2.3b - 4.1) - (7b + 0.7), we need to simplify the expression by using the distributive property and combining like terms.
Step 1: Apply the distributive property by multiplying 5 to each term inside the parentheses:
5 * -2.3b = -11.5b
5 * -4.1 = -20.5
So now our expression becomes:
-11.5b - 20.5 - (7b + 0.7)
Step 2: Apply the distributive property again by multiplying -1 to each term inside the parentheses:
-1 * 7b = -7b
-1 * 0.7 = -0.7
So now our expression becomes:
-11.5b - 20.5 - 7b - (-0.7)
Step 3: Simplify by combining like terms:
-11.5b - 7b = -18.5b
-20.5 - (-0.7) = -19.8
Therefore, the equivalent expression is -18.5b - 19.8, which is closest to answer choice C) -18.5b - 3.4.
To simplify the expression 5(−2.3b − 4.1) − (7b + 0.7):
1) Distribute the 5 to both terms inside the parentheses:
5 * -2.3b = -11.5b
5 * -4.1 = -20.5
So now the expression is:
-11.5b - 20.5 - (7b + 0.7)
2) Remove the parentheses around the second term:
-11.5b - 20.5 - 7b - 0.7
3) Combine like terms:
-11.5b - 7b = -18.5b
-20.5 - 0.7 = -21.2
The equivalent expression is:
-18.5b - 21.2
Therefore, the correct answer is: −18.5b − 21.2.