Question

use the distributive property to solve the equation.
\\(\frac{3}{4}(8a + 12) = 28.2\\)
\\(\left(\frac{3}{4} \cdot \square\
ight) + \left(\square \cdot 12\
ight) = \square\\)
\\(a = \square\\)
(simplify your answers.)

Explanation:

Step1: Apply Distributive Property

The distributive property is \( \frac{3}{4}(8a + 12)=\frac{3}{4}\cdot8a+\frac{3}{4}\cdot12 \). So the first box is \( 8a \), the second box is \( \frac{3}{4} \), and the right - hand side of the equation after distribution is \( \frac{3}{4}\times8a+\frac{3}{4}\times12 \). Calculate \( \frac{3}{4}\times8a = 6a \) and \( \frac{3}{4}\times12 = 9 \), so the equation becomes \( 6a + 9=28.2 \).

Step2: Solve for a

Subtract 9 from both sides of the equation \( 6a+9 - 9=28.2 - 9 \), which gives \( 6a = 19.2 \). Then divide both sides by 6: \( a=\frac{19.2}{6}=3.2 \).

Answer:

The first box: \( 8a \), the second box: \( \frac{3}{4} \), the third box: \( 28.2 \), and \( a = 3.2 \)