Sure, let's solve the given inequality step-by-step:
1. Given inequality:
[tex]\[
-4.4 \geq 1.6x - 3.6
\][/tex]
2. Isolate the term with [tex]\(x\)[/tex]:
[tex]\[
-4.4 + 3.6 \geq 1.6x
\][/tex]
3. Simplify the left side:
[tex]\[
-0.8 \geq 1.6x
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 1.6:
[tex]\[
\frac{-0.8}{1.6} \geq x
\][/tex]
Simplifying the division:
[tex]\[
-0.5 \geq x
\][/tex]
or equivalently:
[tex]\[
x \leq -0.5
\][/tex]
So, the solution to the inequality [tex]\( -4.4 \geq 1.6x - 3.6 \)[/tex] is [tex]\( x \leq -0.5 \)[/tex].
### Graphing the Solution Set
To graph this solution:
1. Draw a number line: Mark the point [tex]\(-0.5\)[/tex] on the number line.
2. Closed circle at [tex]\(-0.5\)[/tex]: Because the inequality includes [tex]\(\leq\)[/tex], [tex]\(-0.5\)[/tex] is part of the solution.
3. Shade to the left of [tex]\(-0.5\)[/tex]: Because [tex]\(x\)[/tex] should be less than or equal to [tex]\(-0.5\)[/tex].
The graph would look like this:
[tex]\[
\begin{array}{cccccccccccccccc}
& & & & & & -0.5 && & & & & & & \\
\bullet & \longleftarrow & \longleftarrow & \longleftarrow & \longleftarrow & \longleftarrow & \bullet & \and & & & & & &
\end{array}
\][/tex]
The darkened arrow to the left indicates that all numbers less than [tex]\(-0.5\)[/tex] are included in the solution set. The closed circle at [tex]\(-0.5\)[/tex] shows that [tex]\(-0.5\)[/tex] itself is also part of the solution.
