Question

Which of the following inequalities is equivalent to -4x+2<-22-x?

Answer 1

The option C) 3x>-24 is the correct answer.

Let's solve the given inequality:


`\[-4x + 2 < -22 - x\]`

Combine like terms:


`\[-3x + 2 < -22\]`

Subtract 2 from both sides:


`\[-3x < -24\]`

Divide by -3 (and remember to reverse the inequality sign when dividing by a negative number):


`\[x > 8\]`

So, the equivalent inequality is
`\[3x > -24\].`

Answer 2

`3x>-24`

Explanation:

Given

`-4x+2<-22-x`

Required

Solve for x

`-4x+2<-22-x`

We start by taking like terms

`-4x + x < -22 - 2`

`-3x < -24`

Divide through by -1: Note, the inequality sign will change:

`3x>-24`