4)) A triangle has two sides of length 19.7 and 6.6. What compound inequality describes the possible lengths for the third side, x? 4) Write a compound inequality like 1lt xlt 3 square

## Step 1: Triangle Inequality Theorem<br />### The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This gives us three inequalities.<br />## Step 2: Inequality 1<br />### $19.7 + 6.6 > x \implies 26.3 > x$ or $x < 26.3$<br />## Step 3: Inequality 2<br />### $19.7 + x > 6.6 \implies x > 6.6 - 19.7 \implies x > -13.1$. Since side lengths must be positive, this simplifies to $x>0$.<br />## Step 4: Inequality 3<br />### $6.6 + x > 19.7 \implies x > 19.7 - 6.6 \implies x > 13.1$<br />## Step 5: Combining Inequalities<br />### Combining $x < 26.3$ and $x > 13.1$, we get $13.1 < x < 26.3$.