Question

Solve - > -1 and 40 – 45 –3 and write the solution in interval notation. If there is no solution, type Ø.

Answer 1

Given the inequalities:

`\begin{gathered} (x)/(4)\ge-1\rightarrow(1) \\ -4x-4\le-3\rightarrow(2) \end{gathered}`

The solution to the first inequality:

`\begin{gathered} (x)/(4)\ge-1\rightarrow*4 \\ x\ge-4 \\ x\in\lbrack-4,\infty) \end{gathered}`

The solution to the second inequality:

`\begin{gathered} -4x-4\le-3 \\ -4x\le-3+4 \\ -4x\le1\rightarrow/(-4) \\ x\ge-(1)/(4) \\ x\in\lbrack-(1)/(4),\infty) \end{gathered}`

We will find the intersection between the intervals

So, the answer will be:

`\lbrack-(1)/(4),\infty)`