To determine the type of equation we are dealing with, let's start by simplifying and analyzing the given equation:
The given equation is:
[tex]\[ 4(x + 3) = 40 \][/tex]
First, let's distribute the 4 on the left side:
[tex]\[ 4 \cdot x + 4 \cdot 3 = 40 \][/tex]
[tex]\[ 4x + 12 = 40 \][/tex]
Next, let's isolate the variable [tex]\( x \)[/tex]. We can do this by first subtracting 12 from both sides of the equation:
[tex]\[ 4x + 12 - 12 = 40 - 12 \][/tex]
[tex]\[ 4x = 28 \][/tex]
Then, divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{28}{4} \][/tex]
[tex]\[ x = 7 \][/tex]
Now that we have simplified and solved the equation, we can see that it is of the form [tex]\( ax + b = c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( x \)[/tex] is the variable.
Therefore, the given equation is a linear equation.
So, the type of equation is:
[tex]\[ \boxed{\text{Linear}} \][/tex]
