Question

Solve each compound inequality. Graph your solutions.
5 + m > 4 or 7m< -35

Answer 1

Solving the inequality
`5 + m > 4\: or\: 7m< -35` we get
`\mathbf{m>-1\:or\: \:m<-5}`

The graph of the inequality is shown in figure attached.

Explanation:

We need to Solve each compound inequality
`5 + m > 4\: or\: 7m< -35`

Solving the inequalities

For solving compound inequalities we solve both inequalities simultaneously and find the value of m.

For solving 5+m > 4, we subtract 5 from both sides.

While solving 7m < -35, we divide both sides by 7 to get value of m

Applying these functions we get:

`5 + m > 4\: or\: 7m< -35\\m>4-5\:or\:m<(-35)/(7)\\m>-1\:or\:m<-5`

So, solving the inequality
`5 + m > 4\: or\: 7m< -35` we get
`\mathbf{m>-1\:or\: \:m<-5}`

The graph of the inequality is shown in figure attached.