N - 5 \leqslant 5n - 1 solve the inequality for n and write the answer in simplest form

Question

`n - 5 \leqslant 5n - 1`

solve the inequality for n and write the answer in simplest form

Answer 1

Hello there!

n - 5 ≤ 5n - 1

Solve for n

Let's start by subtracting 5n from both sides

n - 5 - 5n ≤ 5n - 5n - 1

n - 5 - 5n ≤ -1

We need to transfer -5 on the other side, we can do that by adding 5 on both sides

n - 5 - 5n + 5 ≤ -1 + 5

n - 5n ≤ -4

-4n ≤ -4

Finally divide both sides by -4

-4n/-4 ≤ -4/-4

n ≥ -1 (This is the answer)!

Do you know why I changed the sign?


A lot of students failed to remember that rules, which is:
When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the symbol as well. If it was this <, it will change to this >. Got it? Cool!



I hope the steps are clear to understand. If you have questions, feel free to let me know...

As always, I am here to help!