Question

write an equivalent expression by distributing the \−\ sign outside the parentheses: -(-4.6c - 8)

Explanation:

Step1: Recall the distributive property of multiplication over subtraction (or addition) with a negative sign. The rule is that \(-(a - b)= -a + b\) (or more generally, \(-(x + y)= -x - y\), but when there are negative terms inside, we have to be careful with signs). In this case, we have \(-(-4.6c - 8)\), which is equivalent to multiplying each term inside the parentheses by \(-1\).

So, we distribute the \(-1\) to both \(-4.6c\) and \(-8\).

Step2: Multiply \(-1\) with \(-4.6c\) and \(-1\) with \(-8\).

For the first term: \(-1\times(-4.6c) = 4.6c\) (because multiplying two negative numbers gives a positive number).
For the second term: \(-1\times(-8)=8\) (again, two negative numbers multiplied give a positive number).
Putting it together, we get \(4.6c + 8\).

Answer:

\(4.6c + 8\)