Question

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


-1/4
-1/7
1/9
1/7

Answer 1

To solve the equation \( 2(5x + 1) - 2x = 2 - 2(3x + 1) \), we will simplify both sides step-by-step.

### Step 1: Expand both sides

**Left Side:**
\[
2(5x + 1) - 2x = 10x + 2 - 2x = 8x + 2
\]

**Right Side:**
\[
2 - 2(3x + 1) = 2 - (6x + 2) = 2 - 6x - 2 = -6x
\]

### Step 2: Set the simplified equation

Now the equation looks like:
\[
8x + 2 = -6x
\]

### Step 3: Move all \(x\) terms to one side

Add \(6x\) to both sides:
\[
8x + 6x + 2 = 0 \implies 14x + 2 = 0
\]

### Step 4: Isolate \(x\)

Subtract 2 from both sides:
\[
14x = -2
\]

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

### Conclusion

The value of \(x\) that satisfies the equation \( 2(5x + 1) - 2x = 2 - 2(3x + 1) \) is:
\[
\boxed{-\frac{1}{7}}
\]