Sure! Let's solve the inequality [tex]\(-4 > 2x\)[/tex] step by step.
1. Isolate the variable x: To get [tex]\(x\)[/tex] by itself, we need to divide both sides of the inequality by 2.
[tex]\[
\frac{-4}{2} > \frac{2x}{2}
\][/tex]
2. Simplify the inequality:
[tex]\[
-2 > x
\][/tex]
This can be rewritten as:
[tex]\[
x < -2
\][/tex]
So the solution to the inequality is [tex]\(x < -2\)[/tex].
3. Graph the solution on the number line: To graph [tex]\(x < -2\)[/tex], draw an open circle at -2 and shade everything to the left of -2. An open circle indicates that -2 is not included in the solution.
Here is the number line illustration:
[tex]\[
\begin{array}{ccccccccc}
-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\bullet & \bullet & \bullet & \circ & & & & & \\
\end{array}
\][/tex]
In the graph above:
- The open circle at -2 shows that -2 is not included in the solution.
- The shaded region to the left of -2 (indicated by points and the thicker line) represents all [tex]\(x\)[/tex] values that are less than -2.
Therefore, the solution to the inequality [tex]\(-4 > 2x\)[/tex] is [tex]\(x < -2\)[/tex], and this set of values is represented on the number line as described.
