Sure, let's solve the equation step by step.
We need to solve the equation:
[tex]\[ 6(3x + 4) = 4x - 4 \][/tex]
Let's start by distributing the 6 on the left-hand side:
[tex]\[ 6 \cdot 3x + 6 \cdot 4 = 4x - 4 \][/tex]
[tex]\[ 18x + 24 = 4x - 4 \][/tex]
Next, we need to get all the terms involving [tex]\( x \)[/tex] on one side of the equation. Let's subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 18x - 4x + 24 = -4 \][/tex]
[tex]\[ 14x + 24 = -4 \][/tex]
Now, let's isolate the term with [tex]\( x \)[/tex]. Subtract 24 from both sides:
[tex]\[ 14x = -4 - 24 \][/tex]
[tex]\[ 14x = -28 \][/tex]
Divide both sides by 14 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-28}{14} \][/tex]
[tex]\[ x = -2 \][/tex]
So, the solution to the equation is:
[tex]\[ x = -2 \][/tex]
Let's double-check this solution by plugging [tex]\( x = -2 \)[/tex] back into the original equation:
Original equation:
[tex]\[ 6(3x + 4) = 4x - 4 \][/tex]
Substitute [tex]\( x = -2 \)[/tex]:
[tex]\[ 6(3(-2) + 4) = 4(-2) - 4 \][/tex]
[tex]\[ 6(-6 + 4) = -8 - 4 \][/tex]
[tex]\[ 6(-2) = -12 \][/tex]
[tex]\[ -12 = -12 \][/tex]
This confirms that our solution [tex]\( x = -2 \)[/tex] is correct.
Therefore, the correct change in height in inches is:
[tex]\[ x = -2 \][/tex]
