Solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.
$$-9<7x+5\le 11$$

Step 1 ：First, we need to solve the compound inequality. We can do this by breaking it down into two separate inequalities: $-9<7x+5$ and $7x+5\le 11$.

Step 2 ：Let's start with the first inequality $-9<7x+5$. We can solve for $x$ by first subtracting 5 from both sides of the inequality, which gives us $-14<7x$.

Step 3 ：Next, we divide both sides of the inequality by 7 to isolate $x$. This gives us \(-2-2\).

Step 4 ：Now, let's solve the second inequality $7x+5\le 11$. We can solve for $x$ by first subtracting 5 from both sides of the inequality, which gives us $7x\le 6$.

Step 5 ：Next, we divide both sides of the inequality by 7 to isolate $x$. This gives us $x\le \frac{6}{7}$.

Step 6 ：So, the solution to the compound inequality is $x>-2$ and $x\le \frac{6}{7}$. In interval notation, this is $(-2,\frac{6}{7}]$.

Step 7 ：Finally, we check our solution. We can do this by substituting a number from the interval into the original inequality. For example, if we choose $x=0$, we get $-9<7(0)+5\le 11$, which simplifies to $-9<5\le 11$. This is true, so our solution is correct.