Question

Please help me with this problem just wanted to be sure that I am correct in order to help my son to under stand the break down of this problem. I believe that the answer is -3 but I am not sure please help?Solve for x.14x−1/2(4x+6)=3(x−4)−18 Enter your answer in the box.x =

Answer 1

We want to solve for x in the equation

`14x-(1)/(2)\mleft(4x+6\mright)=3\mleft(x-4\mright)-18`

First we expand the brackets in both sides of the equation, this becomes

`\begin{gathered} 14x-(1)/(2)(4x+6)=3(x-4)-18 \\ 14x-2x-3=3x-12-18 \end{gathered}`

Note that the minus sign multiplies the items in the brackets too

Now, we collect like terms we have

`\begin{gathered} 14x-2x-3x=-12-18+3 \\ 9x=-27 \\ \text{divide both sides by 9, we have } \\ (9x)/(9)=(-27)/(9) \\ x=-3 \end{gathered}`

Hence x = -3