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

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 \(7x+5\leq11\).

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 \(7x+5\leq11\). We can solve for \(x\) by first subtracting 5 from both sides of the inequality, which gives us \(7x\leq6\).

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

Step 6 ：So, the solution to the compound inequality is \(x>-2\) and \(x\leq\frac{6}{7}\). 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 \(-9<7(0)+5\leq11\), which simplifies to \(-9<5\leq11\). This is true, so our solution is correct.