Question

Solve for x. Show each step of the solution.4.5(8 - x) + 22 = 102 – 2.5(5x + 24)

Answer 1

The question to solve is:

`4.5\mleft(8-x\mright)+22=102-2.5\mleft(5x+24\mright)`

Remember the distributive rule to simplify this:

`a(b\pm c)=ab\pm ac`

Now, let's go ahead and simplify further:

`\begin{gathered} 4.5(8-x)+22=102-2.5(5x+24) \\ 36-4.5x+22=102-12.5x-60 \\ 58-4.5x=-12.5x+42 \end{gathered}`

Now, we simply take x's to one side and numbers to another and solve for the variable, x.

`\begin{gathered} -4.5x+12.5x=42-58 \\ 8x=-16 \\ x=-(16)/(8) \\ x=-2 \end{gathered}`