Question

Solve the compound an equality. Write the solution in interval notation.

Answer 1

Step 1: Write the two inequalities equations

`4u\text{ + 1 }\leq\text{ -3 -2u }\ge\text{ 10}`

Step 2: Solve the two inequalities separately

`\begin{gathered} 4u\text{ + 1 }\leq\text{ -3} \\ 4u\text{ }\leq\text{ -3 -1 } \\ 4u\text{ }\leq\text{ -4} \\ u\text{ }\leq\text{ }(-4)/(4) \\ u\text{ }\leq\text{ -1} \end{gathered}`
`\begin{gathered} -2u\text{ }\ge\text{ 10} \\ \text{When you divide inequalities by -2, the sign will change} \\ (-2u)/(-2)\text{ }\leq\text{ }(10)/(-2) \\ u\text{ }\leq\text{ -5} \end{gathered}`

Final answer

`(-\infty,\text{ -5\rbrack}`

Or

`\lbrack\text{ x }\leq\text{ -5\rbrack or ( -}\infty,\text{ -5)}`