Sure! Let's solve the inequality \(\(-4 > 2x\)\) step by step.
1. Isolate the variable x: To get \(\(x\)\) by itself, we need to divide both sides of the inequality by 2.
\(\[
\frac{-4}{2} > \frac{2x}{2}
\]\)
2. Simplify the inequality:
\(\[
-2 > x
\]\)
This can be rewritten as:
\(\[
x < -2
\]\)
So the solution to the inequality is \(\(x < -2\)\).
3. Graph the solution on the number line: To graph \(\(x < -2\)\), 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:
\(\[
\begin{array}{ccccccccc}
-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\bullet & \bullet & \bullet & \circ & & & & & \\
\end{array}
\]\)
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 \(\(x\)\) values that are less than -2.
Therefore, the solution to the inequality \(\(-4 > 2x\)\) is \(\(x < -2\)\), and this set of values is represented on the number line as described.
