Question

Solve the compound inequality. Give the solution set in both interval and graph x+6>10 or 5-x>7

Answer 1

SOLUTIONS

Solve the compound inequality. Give the solution set in both interval and graph

`x+6>10,or\text{ }5-x>7`

Step 1 : Solve the equations separately

`\begin{gathered} x+6>10 \\ x>10-6 \\ x>4 \end{gathered}`
`\begin{gathered} 5-x>7 \\ -x>7-5 \\ -x>2 \\ x<-2 \end{gathered}`

Writing out the solutions both in interval form and graphing:

`\begin{gathered} x<-2\text{ }or\text{ }x>4 \\ -2>x>4 \end{gathered}`