First, let's understand the given function [tex]\( k(x) = 5x - 6 \)[/tex].
We are asked to find the expression equivalent to [tex]\((k + k)(4)\)[/tex].
### Step-by-Step Breakdown
1. Evaluate [tex]\(k(4)\)[/tex]:
[tex]\[
k(4) = 5(4) - 6 = 20 - 6 = 14
\][/tex]
2. Combine [tex]\(k(4)\)[/tex] twice to understand [tex]\((k+k)(4)\)[/tex]:
[tex]\((k+k)(4)\)[/tex] means [tex]\(k(4) + k(4)\)[/tex].
3. Compute the value:
[tex]\[
k(4) + k(4) = 14 + 14 = 28
\][/tex]
Therefore, [tex]\((k + k)(4) = 28\)[/tex].
### Verifying Which Expression Matches
1. Evaluate each given option:
- [tex]\(5(4+4)-6\)[/tex]:
[tex]\[
5(8) - 6 = 40 - 6 = 34
\][/tex]
- [tex]\(5(4)-6 + 5(4)-6\)[/tex]:
[tex]\[
(5(4) - 6) + (5(4) - 6) = 14 + 14 = 28
\][/tex]
- [tex]\(54-6+54-6\)[/tex]:
[tex]\[
This simplifies to 48 + 48 = 96
\][/tex]
- [tex]\(5(5(4)-6)-6\)[/tex]:
[tex]\[
5(20 - 6) - 6 = 5(14) - 6 = 70 - 6 = 64
\][/tex]
2. Identify the correct equivalent expression:
The only expression that matches our computed result [tex]\(28\)[/tex] is [tex]\(5(4)-6 + 5(4)-6\)[/tex].
Thus, the equivalent expression for [tex]\((k+k)(4)\)[/tex] is:
[tex]\[ 5(4)-6 + 5(4)-6 \][/tex]
It's clear and precise.
