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F.11 Graph solutions to advanced linear inequalities

[tex]\[ 5 \, G \, C \][/tex]

Solve the inequality and graph the solution.

[tex]\[ 18 \ \textless \ \frac{h - 14}{-1} \][/tex]

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

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Answer :

GinnyAnswer
To solve the inequality [tex]\( 18 < \frac{h - 14}{-1} \)[/tex] and graph the solution, we should follow these steps:

1. Simplify the Inequality:

The given inequality is:
[tex]\[ 18 < \frac{h - 14}{-1} \][/tex]

2. Deal with the Negative Sign:

Since the denominator is [tex]\(-1\)[/tex], this will flip the direction of the inequality when we multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[ 18 < \frac{h - 14}{-1} \implies 18 \cdot -1 > \frac{h - 14}{-1} \cdot -1 \][/tex]
This gives us:
[tex]\[ -18 > h - 14 \][/tex]

3. Isolate the Variable [tex]\( h \)[/tex]:

To isolate [tex]\( h \)[/tex], we add 14 to both sides of the inequality:
[tex]\[ -18 + 14 > h \][/tex]
[tex]\[ -4 > h \][/tex]

This can be rewritten as:
[tex]\[ h < -4 \][/tex]

4. Solution Interpretation:

The solution to the inequality [tex]\( 18 < \frac{h - 14}{-1} \)[/tex] is:
[tex]\[ h < -4 \][/tex]

5. Graph the Solution:

To graph the solution [tex]\( h < -4 \)[/tex]:

- Plot an open circle at [tex]\( h = -4 \)[/tex] on the number line to indicate that [tex]\(-4\)[/tex] is not included in the solution set.
- Shade the region to the left of [tex]\( h = -4 \)[/tex] to represent all values less than [tex]\(-4\)[/tex].

Here is a step-by-step sketching process:

- Draw a number line.
- Locate the point [tex]\(-4\)[/tex] on the number line.
- Place an open circle at [tex]\(-4\)[/tex] (the open circle indicates that [tex]\(-4\)[/tex] is not part of the solution).
- Shade the line to the left of [tex]\(-4\)[/tex] to indicate that all values less than [tex]\(-4\)[/tex] are part of the solution set.

The final graphical representation will show an open circle at [tex]\(-4\)[/tex] with the line shaded to the left, illustrating that [tex]\( h \)[/tex] can take any value less than [tex]\(-4\)[/tex].

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