First, let's understand the function provided: [tex]\( k(x) = 5x - 6 \)[/tex].
The problem requires us to find an expression equivalent to [tex]\((k+k)(4)\)[/tex]. The notation [tex]\((k + k)(4)\)[/tex] suggests the sum of [tex]\( k(4) \)[/tex] and [tex]\( k(4) \)[/tex] evaluated separately, that is:
[tex]\[ (k + k)(4) = k(4) + k(4) \][/tex]
We can start by calculating [tex]\( k(4) \)[/tex]:
[tex]\[ k(4) = 5(4) - 6 = 20 - 6 = 14 \][/tex]
Since we need [tex]\( k(4) + k(4) \)[/tex]:
[tex]\[ k(4) + k(4) = 14 + 14 = 28 \][/tex]
So, [tex]\((k + k)(4) = 28\)[/tex].
Now, let's examine each given expression to determine which one matches 28.
1. [tex]\( 5(4+4)-6 \)[/tex]:
[tex]\[ 5(4+4)-6 = 5(8)-6 = 40-6 = 34 \][/tex]
This is not equivalent to 28.
2. [tex]\( 5(5(4)-6)-6 \)[/tex]:
[tex]\[ 5(5(4)-6)-6 = 5(20-6)-6 = 5(14)-6 = 70-6 = 64 \][/tex]
This is not equivalent to 28.
3. [tex]\( 54-6+54-6 \)[/tex]:
[tex]\[ 54-6+54-6 = 48 + 48 = 96 \][/tex]
This is not equivalent to 28.
4. [tex]\( 5(4)-6+5(4)-6 \)[/tex]:
[tex]\[ 5(4)-6+5(4)-6 = 20-6 + 20-6 = 14 + 14 = 28 \][/tex]
This is indeed equivalent to 28.
Therefore, the expression that is equivalent to [tex]\((k + k)(4)\)[/tex] is:
[tex]\[ 5(4)-6+5(4)-6 \][/tex]
