Question

1. 10n + 8 < 5n - 7 and 5 + 4n ≤ 5n + 9

Explanation:

Step1: Solve the first inequality

Subtract $5n$ from both sides of $10n + 8<5n - 7$:
$10n-5n + 8<5n-5n - 7$, which simplifies to $5n+8<-7$.
Then subtract 8 from both sides: $5n+8 - 8<-7 - 8$, so $5n<-15$.
Divide both sides by 5: $\frac{5n}{5}<\frac{-15}{5}$, getting $n < - 3$.

Step2: Solve the second inequality

Subtract $4n$ from both sides of $5 + 4n\leqslant5n+9$:
$5+4n-4n\leqslant5n-4n + 9$, which simplifies to $5\leqslant n + 9$.
Then subtract 9 from both sides: $5-9\leqslant n+9 - 9$, so $-4\leqslant n$.

Step3: Find the intersection

We need to find $n$ that satisfies both $n < - 3$ and $-4\leqslant n$.
The intersection of $n < - 3$ and $n\geqslant - 4$ is $-4\leqslant n<-3$.

Answer:

$-4\leqslant n<-3$