Question

Which value of x
satisfies the equation
? 2(5x+1)-2x=2-2(3x+1)

Answer 1

To solve the equation \( 2(5x + 1) - 2x = 2 - 2(3x + 1) \), let's start by expanding and simplifying both sides.

1. Expand the left side:
\[
2(5x + 1) = 10x + 2
\]
So, the left side becomes:
\[
10x + 2 - 2x = 8x + 2
\]

2. Expand the right side:
\[
-2(3x + 1) = -6x - 2
\]
So, the right side becomes:
\[
2 - (6x + 2) = 2 - 6x - 2 = -6x
\]

3. Now, rewrite the equation with the simplified expressions:
\[
8x + 2 = -6x
\]

4. To isolate \( x \), add \( 6x \) to both sides:
\[
8x + 6x + 2 = 0
\]
\[
14x + 2 = 0
\]

5. Next, subtract 2 from both sides:
\[
14x = -2
\]

6. Finally, divide both sides by 14:
\[
x = -\frac{2}{14} = -\frac{1}{7}
\]

Thus, the value of \( x \) that satisfies the equation is:
\[
\boxed{-\frac{1}{7}}
\]