Question

Solve for x. 4x-39>-43 and 8x+31<23with an example of a graphic line

Answer 1

Given:

`4x-39>-43and8x+31<23`

Solve the inequality separately,

`\begin{gathered} 4x-39>-43 \\ 4x>-43+39 \\ 4x>-4 \\ x>-1 \end{gathered}`

Also,

`\begin{gathered} 8x+31<23 \\ 8x<23-31 \\ 8x<-8 \\ x<-1 \end{gathered}`

As the given inequality give x > -1 and x < -1 it shows that there is no solution for the given inequality.

The graph is given as,

The red region shows the inequality 4x -39 > -43 and blue region shows 8x +31 < 23.

Answer: Option D.