Answer :

To solve the equation

[tex]\[ \frac{-2}{2x + 4} = 1 \][/tex]

we need to isolate the variable [tex]\( x \)[/tex]. Here are the steps to do it:

1. Multiply both sides by [tex]\( 2x + 4 \)[/tex] to eliminate the fraction:

[tex]\[ \frac{-2}{2x + 4} \cdot (2x + 4) = 1 \cdot (2x + 4) \][/tex]

This simplifies to:

[tex]\[ -2 = 2x + 4 \][/tex]

2. Isolate [tex]\( x \)[/tex] by isolating the term with [tex]\( x \)[/tex]:

First, subtract 4 from both sides:

[tex]\[ -2 - 4 = 2x \][/tex]

This simplifies to:

[tex]\[ -6 = 2x \][/tex]

3. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:

[tex]\[ \frac{-6}{2} = \frac{2x}{2} \][/tex]

This simplifies to:

[tex]\[ x = -3 \][/tex]

So, the solution to the equation

[tex]\[ \frac{-2}{2x + 4} = 1 \][/tex]

is

[tex]\[ x = -3 \][/tex]