Question

solve the linear inequality for n. graph your answer in the number line. then write the solution in inequality notation.
18 ≥ 4(−6n − 10) − 5n
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Expand the right - hand side

$18\geq4\times(-6n)-4\times10 - 5n$
$18\geq - 24n-40 - 5n$

Step2: Combine like terms

$18\geq(-24n - 5n)-40$
$18\geq - 29n-40$

Step3: Add 40 to both sides

$18 + 40\geq - 29n-40 + 40$
$58\geq - 29n$

Step4: Divide both sides by - 29 and reverse the inequality sign

$\frac{58}{-29}\leq\frac{-29n}{-29}$
$- 2\leq n$ or $n\geq - 2$

Answer:

The solution in inequality notation is $n\geq - 2$. To graph on the number - line, place a closed circle at $n=-2$ (since the inequality is $\geq$) and draw a line to the right.