Question

solve the compound Inequalities, graph the solutions and write the solutions in interval notation$4x - 3 \leqslant 13 \: and \: - x - 5 \ \textless \ - 5$

Answer 1

Answer:

The solution is:

$-10OR (-10,4)Explanation:

Given:

[tex]\begin{gathered} 4x-3\le13\ldots\ldots\ldots....\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(1) \\ -x-5<5\ldots\ldots\ldots\ldots\ldots........\ldots.\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}$

From (2), we have:

$x>-10\ldots\ldots\ldots..\ldots\ldots\ldots\ldots\ldots.\ldots.\ldots\text{.}(3)$

Using this (1)

$\begin{gathered} 4x\le16 \\ \\ x\le\frac{16}{4}=4\ldots\ldots\ldots\ldots.......\ldots\ldots\ldots\ldots\ldots\ldots\ldots..(4) \end{gathered}$

The solution now is:

[tex]-10