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

Answer:

{ h | h ≤ 12/7}

( - ∞, 12/7 ]

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:

$\begin{gathered} \frac{-7h}{-7}\leq\frac{-12}{-7} \\ h\leq\frac{12}{7} \end{gathered}$

Therefore, the answer in set-builder notation is:

$\lbrace h|h\leq\frac{12}{7}\rbrace$

And the answer in interval notation is:

$(-\infty,\frac{12}{7}\rbrack$

Finally, The answer in a number line is: