Question

1. what is the solution to this equation: 2(3x + 8) = 4 - 3(-x - 12) type a response

Explanation:

Step1: Expand both sides

First, we expand the left - hand side of the equation \(2(3x + 8)\) using the distributive property \(a(b + c)=ab+ac\). So, \(2(3x + 8)=2\times3x+2\times8 = 6x + 16\).

Then, we expand the right - hand side of the equation \(4-3(-x - 12)\). Using the distributive property \(a(b + c)=ab + ac\) (here \(a=- 3\), \(b=-x\), \(c = - 12\)), we get \(4-3\times(-x)-3\times(-12)=4 + 3x+36\). And \(4 + 36+3x=40 + 3x\).

Now our equation becomes \(6x + 16=40+3x\).

Step2: Isolate the variable \(x\)

Subtract \(3x\) from both sides of the equation \(6x + 16=40 + 3x\).
\(6x-3x + 16=40+3x-3x\), which simplifies to \(3x+16 = 40\).

Then subtract 16 from both sides: \(3x+16 - 16=40 - 16\).
\(3x=24\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x = 24\) by 3.
\(\frac{3x}{3}=\frac{24}{3}\), so \(x = 8\).

Answer:

\(x = 8\)