1. **State the problem:** We need to determine which of the given equations are true when $x=8$. 2. **List the equations:** - $\frac{7}{9}x = 6 \frac{2}{9}$ - $x + 11.5 = 20.5$ - $23.42 - x = 15.42$ - $11x = 88$ - $\frac{x}{48} = 6$ 3. **Evaluate each equation by substituting $x=8$: ** **Equation 1:** $$\frac{7}{9} \times 8 = \frac{56}{9} = 6 \frac{2}{9}$$ Since $6 \frac{2}{9} = \frac{56}{9}$, this equation is true. **Equation 2:** $$8 + 11.5 = 19.5 \neq 20.5$$ So, this equation is false. **Equation 3:** $$23.42 - 8 = 15.42$$ $$15.42 = 15.42$$ This equation is true. **Equation 4:** $$11 \times 8 = 88$$ $$88 = 88$$ This equation is true. **Equation 5:** $$\frac{8}{48} = \frac{1}{6} \neq 6$$ This equation is false. 4. **Final answer:** The true equations when $x=8$ are: - $\frac{7}{9}x = 6 \frac{2}{9}$ - $23.42 - x = 15.42$ - $11x = 88$