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) \\ ((a+8)(x+6))/((x+6))=(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`