Question

78: 5 - 3a >= 8 or 2a +1> 7

Answer 1

In order to solve the system of inequalities, let's solve each inequation for 'a':

`\begin{gathered} 5-3a\ge8 \\ -3a\ge8-5 \\ -3a\ge3 \\ 3a\le-3 \\ a\le-1 \\ \\ 2a+1>7 \\ 2a>7-1 \\ 2a>6 \\ a>3 \end{gathered}`

So, the answer to this system is:

`\begin{gathered} \text{set}-\text{builder notation:} \\ \mleft\lbrace a\mright|a\le-1\text{ or }a>3\} \\ \\ \text{interval notation:} \\ (-\infty,-1\rbrack\cup(3,\infty) \end{gathered}`