If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?

To find which expression is equivalent to \((k + k)(4)\), we first need to evaluate \(k(4)\):

Given \(k(x) = 5x - 6\), we calculate:

\[ k(4) = 5(4) - 6 = 20 - 6 = 14 \]

Now, \(k + k\) means \(k(x) + k(x)\):

\[ k + k = k(4) + k(4) = 14 + 14 = 28 \]

Thus, we need to evaluate \((k + k)(4)\):

\[ (k + k)(4) = 28 \]

Now we will evaluate each of the provided expressions to see which one equals 28:

1. Expression 1: \(5(4 + 4) - 6\)

\[ = 5(8) - 6 = 40 - 6 = 34 \]

2. Expression 2: \(5(5(4) - 6) - 6\)

Calculating \(5(4) - 6\):

\[ 5(4) - 6 = 20 - 6 = 14 \] Then, \[ 5(14) - 6 = 70 - 6 = 64 \]

3. Expression 3: \(54 - 6 + 54 - 6\)

\[ = 54 + 54 - 12 = 108 - 12 = 96 \]

4. Expression 4: \(5(4) - 6 + 5(4) - 6\)

Calculating \(5(4) - 6\):

\[ 5(4) - 6 = 20 - 6 = 14 \] Then, it becomes: \[ 14 + 14 = 28 \]

The only expression that is equal to 28 is:

Expression 4: \(5(4) - 6 + 5(4) - 6\)