Question

9. -10(c + 3) + 4c = 90

Answer 1

Consider the given inequation,

`-10(c+3)+4c\ge90`

Resolve the parenthesis first,

`\begin{gathered} -10(c)-10(3)+4c\ge90 \\ -10c-30+4c\ge90 \end{gathered}`

Adding the like terms,

`\begin{gathered} (-10+4)c-30\ge90 \\ -6c-30\ge90 \end{gathered}`

Add 30 both sides,

`\begin{gathered} -6c-30+30\ge90+30 \\ -6c\ge120 \end{gathered}`

Divide both sides by -6, note that the inequality gets reversed when multiplied or divided by a negative number,

`\begin{gathered} (-6c)/(-6)\leq(120)/(-6) \\ c\leq-20 \end{gathered}`

Thus, the solution set for the given inequation is,

`c\in(-\infty,-20\rbrack`