Question

Which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)?OA.X>-4OB.X<-4O C.x>-3ODX<-3

Answer 1

The given expression is

`10\mleft(3x+2\mright)>7\mleft(2x-4\mright)`

First, we use the distributive property

`\begin{gathered} 10\cdot3x+10\cdot2>7\cdot2x-7\cdot4 \\ 30x+20>14x-28 \end{gathered}`

Now, we subtract 20 on each side

`\begin{gathered} 30x+20-20>14x-28-20 \\ 30x>14x-48 \end{gathered}`

Then, we subtract 14x on each side

`\begin{gathered} 30x-14x>14x-48-14x \\ 16x>-48 \end{gathered}`

At last, we divide the equation by 16

`\begin{gathered} (16x)/(16)>(-48)/(16) \\ x>-3 \end{gathered}`

Therefore, the inequality that represents all solutions is x > -3.