Question

If the replacement set is the set of integers lying between $-4$ and $8$, then find the solution set of $14-5x\ge 3x-40$. Also, represent the solution set on number line.

Answer 1

Step 1: Solve the given inequality

$$\begin{gathered} \Rightarrow 14-5x\ge 3x-40 \\ \Rightarrow 14+40\ge 3x+5x \\ \Rightarrow 54\ge 8x \\ \Rightarrow x\le \frac{54}{8} \\ \Rightarrow x\le 6.75 \end{gathered}$$

Step 2: Identify the solution set between the given replacement set

The given replacement set lies between $-4$ and $8$.

Thus, the required solution set will be $x\in \{-3,-2,-1,0,1,2,3,4,5,6\}$

Step 3: Represent the solution set on number line

Hence, the solution set is $\mathbf{\{}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{,}\mathbf{5}\mathbf{,}\mathbf{6}\mathbf{\}}$.