Question

Solve the inequality and graph the solution set. Write the solution set in (a) set-builder notation and (b) interval notation. Expressnumbers in simplest form.-7h+1>= -11

Answer 1

h

( - ∞, 12/7 ]

Step-by-step explanation:

To solve the inequality we need to subtract 1 on both sides as:

`\begin{gathered} -7h+1\ge-11 \\ -7h+1-1\ge-11-1 \\ -7h\ge-12 \end{gathered}`

Now, dividing by -7, we get:

Remember that when we multiply or divide by a negative number, the sign of the inequality change, so:

`\begin{gathered} (-7h)/(-7)\leq(-12)/(-7) \\ h\leq(12)/(7) \end{gathered}`

Therefore, the answer in set-builder notation is:

`\lbrace h|h\leq(12)/(7)\rbrace`

And the answer in interval notation is:

`(-\infty,(12)/(7)\rbrack`

Finally, The answer in a number line is: