We are asked to solve the inequality
[tex]10-4|1-8n|\leq6[/tex]which can be decomposed into two separate inequalities
[tex]10-4(1-8n)\leq6[/tex]and
[tex]10+4(1-8n)\leq6[/tex]Let us solve the first inequality. by first subtracting 10 from both sides. Doing this gets us
[tex]-4\mleft(1-8n\mright)\le-4[/tex]dividing both sides by -4 reverses the sign of the inequality; therefore, we get
[tex]1-8n\ge1[/tex]subtracting 1 from both sides gets us
[tex]-8n>0[/tex][tex]\textcolor{#FF7968}{\therefore n\leq0}[/tex]A similar process for the inequality 10 + 4(1-8n) ≤ 6 gives us the solution
[tex]\textcolor{#FF7968}{n\ge\frac{1}{4}}[/tex]
