Question

Solve the compound inequality and give your answer in interval notation.7x - 4 <3 OR – 7x+8<34ha

Answer 1

`\begin{gathered} 7x-4<3OR-7x+8\leq-34 \\ 7x<3+4OR-7x\leq-34-8 \\ 7x<7OR-7x\leq-42 \\ \text{Divide the left inequality by 7 and the right side one by -7} \\ x<1\text{ OR x }\ge6 \\ \text{The compound inequalty can now be written out as follows;} \\ 1>x\ge6 \\ In\text{ interval notation, this becomes;} \\ x(\infty,\text{ 1)} \\ x\lbrack6,\infty\rbrack \end{gathered}`