Question

Solve for x:(x+1)(x+5) = x(x+10)

Answer 1

First, we apply distributive property as:

`\begin{gathered} (x+1)(x+5)=x(x+10) \\ (x\cdot x)+(x\cdot5)+(1\cdot x)+(1\cdot5)=(x\cdot x)+(10\cdot x) \\ x^2+5x+x+5=x^2+10x \end{gathered}`

Then, adding like terms:

`x^2+6x+5=x^2+10x`

Subtracting x² from both sides:

`\begin{gathered} x^2+6x+5-x^2=x^2+10x-x^2 \\ 6x+5=10x \end{gathered}`

Subtracting 6x from both sides:

`\begin{gathered} 6x+5-6x=10x-6x \\ 5=4x \end{gathered}`

Finally, dividing by 4:

`\begin{gathered} (5)/(4)=(4x)/(4) \\ 1.25=x \end{gathered}`

Answer: x