Question

An inequality is shown: −np − 4 ≤ 2(c − 3) Which of the following solves for n?

Answer 1

`\huge\boxed{n\leq(2-2c)/(p)\ \text{for}\ p<0}\\\boxed{n\geq(2-2c)/(p)\ \text{for}\ p>0}`

Explanation:

`-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\\eq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq(2-2c)/(p)}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq(2-2c)/(p)}`