Question

6(x+1)-__(8x+5)= -26x-14Fill in the blank

Answer 1

Given the equation below:

Let the blank be the letter y.

`6\left(x+1\right)-_{}y(8x+5)_{}=-26x-14`

We are required to fill in the blank to make the equation true.

We can re-write the equation as:

`\begin{gathered} 6x+6-8xy-5y_{}=-26x-14 \\ (6x-8xy)+(6-5y)=-26x-14 \end{gathered}`

Comparing the left-hand side and right-hand side of the equation: (Taking coefficients of x), we have:

`\begin{gathered} 6x-8xy=-26x \\ -8xy=-26x-6x \\ -8xy=-32x \\ \text{Divide both sides by -8x} \\ y=4 \end{gathered}`

Therefore, we can fill the blank with the number 4.

Thus:

`6\left(x+1\right)-_{}4(8x+5)_{}=-26x-14`