Question

Solve the compound inequality2x75 - 1 and 4xsOSelect the correct choice below and, if necessary, fill in the answer bO A. The solution set is(Type your answer in interval notation. Simplify your answer.O B. The solution set is Ø.A

Answer 1

step 1

Solve the inequality 1

`\begin{gathered} 2x+7\leq-1 \\ 2x\leq-1-7 \\ 2x\leq-8 \\ x\leq-4 \end{gathered}`

the solution of the inequality 1 is the interval

(-infinite, -4}

step 2

solve the inequality 2

`\begin{gathered} 4x\leq0 \\ x\leq0 \end{gathered}`

the solution of the inequality 2 is the interval (-infinite, 0}

step 3

Find the solution of the inequality 1 and the inequality 2

`\mleft(-infinite,-4\mright)\text{ }\cap\text{ }\mleft(-infinite,0\mright)=(-infinite,-4)`

therefore

the solution set is (-infinite, -4}