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35 votes
35 votes
21) 10 - 4 1 - 811 56 -7 -6 -5 -3 -2 -1 0 1 2 3 4 5

User Emil Eriksson
by
2.5k points

1 Answer

8 votes
8 votes

We are asked to solve the inequality


10-4|1-8n|\leq6

which can be decomposed into two separate inequalities


10-4(1-8n)\leq6

and


10+4(1-8n)\leq6

Let us solve the first inequality. by first subtracting 10 from both sides. Doing this gets us


-4\mleft(1-8n\mright)\le-4

dividing both sides by -4 reverses the sign of the inequality; therefore, we get


1-8n\ge1

subtracting 1 from both sides gets us


-8n>0
\textcolor{#FF7968}{\therefore n\leq0}

A similar process for the inequality 10 + 4(1-8n) ≤ 6 gives us the solution


\textcolor{#FF7968}{n\ge(1)/(4)}

User Siddhu
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2.9k points