Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -2(-c - 8) = -8c + 6 2c + 16 = -8c + 6 + 16 = 6 add 8c to both sides 10c = -10 c = divide both sides by 10

Explanation:

Step1: Expand the left - hand side

We use the distributive property \(a(b + c)=ab+ac\). Here, \(-2(-c - 8)=(-2)\times(-c)+(-2)\times(-8)=2c + 16\).

Step2: Add \(8c\) to both sides

Starting from \(2c + 16=-8c + 6\), when we add \(8c\) to both sides, we get \((2c+8c)+16=(-8c + 8c)+6\), which simplifies to \(10c+16 = 6\).

Step3: Subtract 16 from both sides

From \(10c+16 = 6\), subtracting 16 from both sides gives \(10c+16-16=6 - 16\), so \(10c=-10\).

Step4: Divide both sides by 10

Dividing both sides of \(10c=-10\) by 10, we have \(\frac{10c}{10}=\frac{-10}{10}\), so \(c=-1\).

Answer:

The first blank is \(10c\), the second blank is "Subtract 16 from both sides", and \(c=-1\).