Let's solve the equation step-by-step:
Given equation:
[tex]\[ 7x - 7 = 9x - 23 \][/tex]
### Step 1: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side
First, we need to isolate the [tex]\( x \)[/tex] terms on one side. To do this, we can subtract [tex]\( 9x \)[/tex] from both sides:
[tex]\[ 7x - 7 - 9x = -23 \][/tex]
Next, let's combine the [tex]\( x \)[/tex] terms on the left side:
[tex]\[ 7x - 9x - 7 = -23 \][/tex]
### Step 2: Combine like terms
Simplifying the [tex]\( x \)[/tex] terms, we get:
[tex]\[ -2x - 7 = -23 \][/tex]
Next, we need to move the constant term [tex]\(-7\)[/tex] to the other side of the equation by adding [tex]\( 7 \)[/tex] to both sides:
[tex]\[ -2x - 7 + 7 = -23 + 7 \][/tex]
This simplifies to:
[tex]\[ -2x = -16 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\(-2\)[/tex]
To isolate [tex]\( x \)[/tex], we divide both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[ x = \frac{-16}{-2} \][/tex]
Simplifying the division, we get:
[tex]\[ x = 8 \][/tex]
So the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{8} \][/tex]
