Solve the Absolute Value Equation: Find X in |2x + 6| = 1

To solve the absolute value equation $|2x + 6| = 1$, we must consider the definition of absolute value.

• Step 1: Set up two separate equations corresponding to the positive and negative scenarios:
• Equation 1: $2x + 6 = 1$
• Equation 2: $2x + 6 = -1$
• Step 2: Solve each equation independently for $x$.

Solving Equation 1:
Start with $2x + 6 = 1$.
Subtract 6 from both sides: $2x = 1 - 6$.
Thus, $2x = -5$.
Divide both sides by 2: $x = -\frac{5}{2}$ or $x = -2.5$.

Solving Equation 2:
Start with $2x + 6 = -1$.
Subtract 6 from both sides: $2x = -1 - 6$.
Thus, $2x = -7$.
Divide both sides by 2: $x = -\frac{7}{2}$ or $x = -3.5$.

Combining both results, the solutions to the equation $|2x + 6| = 1$ are:

$x = -2.5$ and $x = -3.5$.