x_(A) A triangle has two sides of length 11.6 and 1.2. What compound inequality describes the possible lengths for the third side, x? 1) Write a compound inequality like 1lt xlt 3 square

## Step 1: Triangle Inequality Theorem<br />### The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.<br /><br />## Step 2: Setting up the Inequalities<br />### Let the two given sides be $a = 11.6$ and $b = 1.2$. Let the third side be $x$. We can set up three inequalities:<br />$a + b > x \Rightarrow 11.6 + 1.2 > x \Rightarrow 12.8 > x$<br />$a + x > b \Rightarrow 11.6 + x > 1.2 \Rightarrow x > -10.4$<br />$b + x > a \Rightarrow 1.2 + x > 11.6 \Rightarrow x > 10.4$<br /><br />## Step 3: Combining the Inequalities<br />### Since a side length must be positive, $x > -10.4$ is redundant. Combining $12.8 > x$ and $x > 10.4$, we get $10.4 < x < 12.8$.