Question

first, simplify the equation by using the distributive property.
2(6a + 9) = 3(4a + 6)
a + ? = ?a + ?
distribute.

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), for the left - hand side \(2(6a + 9)\), we have \(2\times6a+2\times9 = 12a+18\). For the right - hand side \(3(4a + 6)\), we have \(3\times4a+3\times6=12a + 18\). So the equation becomes \(12a+18=12a + 18\).

Step2: Subtract \(12a\) from both sides

\((12a+18)-12a=(12a + 18)-12a\). Using the commutative and associative properties of addition \((12a-12a)+18=(12a-12a)+18\). Since \(12a-12a = 0\), we get \(0 + 18=0+18\) or \(18 = 18\).

Answer:

The simplified form is \(12a+18 = 12a+18\) (after expansion) and then \(18=18\) (after subtracting \(12a\) from both sides). This equation is an identity, meaning it is True for all values of \(a\).