Question

Match the inequality to the graph of its solution

Column 1	Column 2
$c+7\le 3$
$c-3>1$
$c-7<3$

Answer 1

Step-1: Explanation of A:

Solving the equation

$c+7\le 3$

Subtracting $7$ from both sides of the equation

$$\begin{gathered} \Rightarrow c+7-7\le 3-7 \\ \Rightarrow c\le -4 \end{gathered}$$

Therefore, $c$ lies in the interval $(-\infty ,-4]$

Plotting in the graph

Marked in the graph, it shows

Therefore, $\left(A\right)\to \left(II\right)$

Step-2: Explanation of B:

$c-3>1$

Adding $3$ on both sides of the equation

$$\begin{gathered} c-3+3>1+3 \\ \Rightarrow c>4 \end{gathered}$$

Therefore, $c$ lies in the interval $(4,\infty )$

Plotting in the graph

Marked in the graph, it shows

Hence, $\left(B\right)\to \left(III\right)$

Step-3: Explanation of C:

$c-7<3$

Adding $3$ on both sides of the equation

$$\begin{gathered} c-7+7<3+7 \\ \Rightarrow c<10 \end{gathered}$$

Therefore, $c$ lies in the interval $(-\infty ,10)$

Plotting in the graph

Marked in the graph, it shows

Hence, $\left(C\right)\to \left(I\right)$

Hence,

$$\begin{gathered} \left(A\right)\to \left(II\right) \\ \left(B\right)\to \left(III\right) \\ \left(C\right)\to \left(I\right) \end{gathered}$$