Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -2(-8c + 2) + 3 = -1 16c - 4 + 3 = -1 16c - \boxed{} = -1 16c = 0 c = \boxed{} \text{combine like terms} \text{divide both sides by 16}

Explanation:

Step1: Distribute the -2

We start with the equation \(-2(-8c + 2) + 3 = -1\). Using the distributive property \(a(b + c)=ab+ac\), we have \(-2\times(-8c)+(-2)\times2 + 3=-1\), which simplifies to \(16c-4 + 3=-1\). So the first missing description is "Distribute the -2".

Step2: Combine like terms

Now, combine the constant terms \(-4\) and \(3\). \(-4 + 3=-1\), so the equation becomes \(16c-1=-1\). Thus, the missing term in \(16c-\square=-1\) is \(1\).

Step3: Add 1 to both sides

To isolate the term with \(c\), we add \(1\) to both sides of the equation \(16c - 1=-1\). So \(16c-1 + 1=-1 + 1\), which simplifies to \(16c = 0\). The missing description here is "Add 1 to both sides".

Step4: Divide both sides by 16

Finally, divide both sides of \(16c = 0\) by \(16\). \(\frac{16c}{16}=\frac{0}{16}\), so \(c = 0\).

Answer:

• The first missing description: Distribute the -2
• The missing term in \(16c-\square=-1\): \(1\)
• The missing description for \(16c = 0\): Add 1 to both sides
• The value of \(c\): \(0\)