want to know if this right solve the inequality and represent your answer in set buldier notation 30n+6<6(4n+7)
30 n+6<24n+42
30+24n-24n<24n-24n+42
6n+6<42-6
6n<36
6n/6<36/6
n<6
set builder is {n/n,6}
yes it looks correct to me, just make sure in your third line not to leave off the n for 30n and keep your +6 in there
To solve the inequality 30n + 6 < 6(4n + 7), follow these steps:
1. Distribute the 6 on the right side of the inequality: 6(4n + 7) = 24n + 42
So, the inequality becomes: 30n + 6 < 24n + 42
2. Subtract 24n from both sides of the inequality to isolate the variable term: 30n - 24n + 6 < 24n - 24n + 42
Simplifying, we get: 6n + 6 < 42
3. Subtract 6 from both sides of the inequality: 6n + 6 - 6 < 42 - 6
This gives us: 6n < 36
4. Divide both sides of the inequality by 6 to solve for n: (6n) / 6 < 36 / 6
The inequality simplifies to: n < 6
Therefore, the solution to the inequality is n < 6.
Now to represent the answer in set-builder notation, we express it as {n | n < 6}.
The vertical bar "|" means "such that" and separates the variable (n) from the condition (n < 6).
In other words, we are specifying that n is an element of the set, and it must be less than 6 in this case.