Question

Fill in the blank __(x+6)+8(x+6) =4x+24

Answer 1

We want to fill in the blank in the equation;

let's represent the blank with a.

$_{}a(x+6)+8(x+6)=4x+24$

Let's factorize the right side of the equation.

$\begin{gathered} a(x+6)+8(x+6)=4x+24 \\ a(x+6)+8(x+6)=4(x+6) \end{gathered}$

and also the left side;

$\begin{gathered} a(x+6)+8(x+6)=4(x+6) \\ (a+8)(x+6)=4(x+6) \end{gathered}$

Then let's divide both sides by (x+6);

$\begin{gathered} (a+8)(x+6)=4(x+6) \\ \frac{(a+8)(x+6)}{(x+6)}=\frac{4(x+6)}{(x+6)} \\ (a+8)=4 \end{gathered}$

Then we can solve for a in the resulting equation.

subtract 8 from both sides.

$\begin{gathered} a+8=4 \\ a+8-8=4-8 \\ a=-4 \end{gathered}$

Therefore, the value to fill into the blank is -4

$-4(x+6)+8(x+6)=4x+24$