Question

What value of x makes this equation true?
2 (3x - 8) = 2 (7x + 2)

Answer 1

To solve the equation \(2 (3x - 8) = 2 (7x + 2)\), we can start by simplifying both sides.

1. Distribute the 2 on both sides:
\[
2 \cdot (3x - 8) = 6x - 16
\]
\[
2 \cdot (7x + 2) = 14x + 4
\]

So, the equation now looks like this:
\[
6x - 16 = 14x + 4
\]

2. Next, we want to isolate \(x\). Let's start by getting all terms involving \(x\) on one side and constant terms on the other side. We can subtract \(6x\) from both sides:
\[
-16 = 14x - 6x + 4
\]
This simplifies to:
\[
-16 = 8x + 4
\]

3. Now, subtract 4 from both sides to isolate the term with \(x\):
\[
-16 - 4 = 8x
\]
Which gives us:
\[
-20 = 8x
\]

4. Finally, divide both sides by 8 to solve for \(x\):
\[
x = \frac{-20}{8} = \frac{-5}{2}
\]

Thus, the value of \(x\) that makes the original equation true is:
\[
\boxed{-\frac{5}{2}}
\]