Question

Please help me step by step on how to get the answer.1.Solve for x. Show each step to the solution. 4.5(8 – x) + 22 = 102 – 2.5(5x + 24)

Answer 1

The given equation is,

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

Solving for x

Expanding both sides of the equation

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

Collect like terms

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

Divide both sides by 8

`\begin{gathered} (8x)/(8)=-(16)/(8) \\ x=-2 \end{gathered}`

Hence,

`x=-2`