Solve the following linear inequalities using the given graph.
6-3x ≤ -12
On the same graph, we draw the lines whose equations are:
\begin{cases} y=6-2x \cr \cr y=12 \end{cases}
We can see on the graph that the lines intersect at \left(6,-12\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is [6,\infty).
2x-4 \le -2
On the same graph, we draw the lines whose equations are:
\begin{cases} y=2x-4 \cr \cr y=-2\end{cases}
We can see on the graph that the lines intersect at \left(1,-2\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is (-\infty,1].
4x-6 \le x
On the same graph, we draw the lines whose equations are:
\begin{cases} y=4x-6 \cr \cr y=x \end{cases}
We can see on the graph that the lines intersect at \left(2{,}2\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is (-\infty,2].
5x-24 \ge -x
On the same graph, we draw the lines whose equations are:
\begin{cases} y=-x \cr \cr y=5x-24 \end{cases}
We can see on the graph that the lines intersect at \left(4,-4\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is [4,\infty).
2x-3 \ge -1
On the same graph, we draw the lines whose equations are:
\begin{cases} y=-1 \cr \cr y=2x-3 \end{cases}
We can see on the graph that the lines intersect at \left(1,-1\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is [1,\infty).
1-4x \ge -3
On the same graph, we draw the lines whose equations are:
\begin{cases} y=-3 \cr \cr y=1-4x \end{cases}
We can see on the graph that the lines intersect at \left(1,-3\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is (-\infty,1].
3x-5 \ge 4
On the same graph, we draw the lines whose equations are:
\begin{cases} y= 4 \cr \cr y=3x-5 \end{cases}
We can see on the graph that the lines intersect at \left(3{,}4\right). The area in which the inequality holds is above the first line and below the second line (the green area).
The set of solutions is [3,\infty).