The solution to the given inequality is k > -18
From the question,
We are to solve the given inequality
The given inequality is [tex]-8 <\frac{2}{5} (k-2)[/tex]
To solve the given inequality, we will determine the value of the variable. The variable in the given inequality is k.
The inequality can be solved as shown below
[tex]-8 <\frac{2}{5} (k-2)[/tex]
First, Multiply through by 5
[tex]5\times -8 <5 \times \frac{2}{5} (k-2)[/tex]
[tex]-40 <2 (k-2)[/tex]
Now, clear the bracket by distributing 2
[tex]-40 < 2k -4[/tex]
[tex]-40+4<2k[/tex]
[tex]-36 <2k[/tex]
Reversing the inequality, we get
[tex]2k>-36[/tex]
(Note the change in sign)
Now, divide both sides by 2
[tex]\frac{2k}{2} >\frac{-36}{2}[/tex]
[tex]k > -18[/tex]
Hence, the solution to the given inequality is k > -18
Learn more on solving inequalities here: https://brainly.com/question/18881247
