Show that the following equations are true, by using the distributive property. a. \( 3 \times(2+6)=(3 \times 2)+(3 \times 6) \) \( \begin{array}{l}0.5 \times(3+3)=(5 \times 3)+(5 \times 3) \\ \end{array} \)

Sure! Let's verify both equations using the **distributive property**. The distributive property states that for any numbers \( a \), \( b \), and \( c \): \[ a \times (b + c) = (a \times b) + (a \times c) \] ### a. \( 3 \times (2 + 6) = (3 \times 2) + (3 \times 6) \) **Step 1: Calculate the left side of the equation** \[ 3 \times (2 + 6) \] \[ = 3 \times 8 \] \[ = 24 \] **Step 2: Calculate the right side of the equation** \[ (3 \times 2) + (3 \times 6) \] \[ = 6 + 18 \] \[ = 24 \] **Conclusion:** Both sides equal **24**, so the equation holds true. --- ### b. \( 0.5 \times (3 + 3) = (0.5 \times 3) + (0.5 \times 3) \) *Note: It seems there was a minor typo in your original equation where \( 5 \times 3 \) was written instead of \( 0.5 \times 3 \). We'll proceed with \( 0.5 \times 3 \).* **Step 1: Calculate the left side of the equation** \[ 0.5 \times (3 + 3) \] \[ = 0.5 \times 6 \] \[ = 3 \] **Step 2: Calculate the right side of the equation** \[ (0.5 \times 3) + (0.5 \times 3) \] \[ = 1.5 + 1.5 \] \[ = 3 \] **Conclusion:** Both sides equal **3**, so the equation holds true. --- **Summary:** Using the distributive property, we've shown that both equations are valid: 1. \( 3 \times (2 + 6) = (3 \times 2) + (3 \times 6) \) 2. \( 0.5 \times (3 + 3) = (0.5 \times 3) + (0.5 \times 3) \) Both equations simplify to the same result on each side, confirming their validity.