If [tex]$k(x) = 5x - 6$[/tex], which expression is equivalent to [tex](k+k)(4)[/tex]?

A. [tex]5(4 + 4) - 6[/tex]
B. [tex]5(5(4) - 6) - 6[/tex]
C. [tex]54 - 6 + 54 - 6[/tex]
D. [tex]5(4) - 6 + 5(4) - 6[/tex]



Answer :

Let's analyze the given function and the expressions step-by-step to determine which expression is equivalent to [tex]\((k + k)(4)\)[/tex]:

1. Understand the function [tex]\(k(x)\)[/tex]:
Given:
[tex]\[ k(x) = 5x - 6 \][/tex]

2. Evaluate the function [tex]\(k(x)\)[/tex] at [tex]\(x = 4\)[/tex]:
[tex]\[ k(4) = 5(4) - 6 = 20 - 6 = 14 \][/tex]

3. Understand what [tex]\((k + k)(4)\)[/tex] means:
[tex]\((k + k)(4)\)[/tex] is equivalent to:
[tex]\[ k(4) + k(4) \][/tex]
Since we already found that [tex]\(k(4) = 14\)[/tex], we have:
[tex]\[ k(4) + k(4) = 14 + 14 = 28 \][/tex]

4. Now let's analyze each provided expression to see which one evaluates to 28:

- Expression 1: [tex]\(5(4 + 4) - 6\)[/tex]
[tex]\[ 5(4 + 4) - 6 = 5(8) - 6 = 40 - 6 = 34 \][/tex]
This evaluates to 34, not 28.

- Expression 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 evaluates to 64, not 28.

- Expression 3: [tex]\(54 - 6 + 54 - 6\)[/tex]
[tex]\[ 54 - 6 + 54 - 6 = 48 + 48 = 96 \][/tex]
This evaluates to 96, not 28.

- Expression 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 evaluates to 28, which matches our computed value for [tex]\((k + k)(4)\)[/tex].

Therefore, the expression that is equivalent to [tex]\((k + k)(4)\)[/tex] is:
[tex]\[ 5(4) - 6 + 5(4) - 6 \][/tex]