High School

Graph the solutions of the inequality:

[tex]47 \geq x + 24[/tex]

Choose the correct graph below.

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B.
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F.

Answer :

To solve the inequality [tex]\(47 \geq x + 24\)[/tex] and graph the solutions, we can follow these steps:

1. Isolate the variable [tex]\(x\)[/tex]:
Start by subtracting 24 from both sides of the inequality to solve for [tex]\(x\)[/tex].

[tex]\[
47 - 24 \geq x
\][/tex]

2. Simplify the inequality:
Calculate the difference on the left side.

[tex]\[
23 \geq x
\][/tex]

3. Rewrite the solution:
The inequality [tex]\(23 \geq x\)[/tex] can be rewritten as [tex]\(x \leq 23\)[/tex].

4. Graph the solution:
On a number line, [tex]\(x \leq 23\)[/tex] means that [tex]\(x\)[/tex] can take any value less than or equal to 23. To graph this, we:

- Place a closed circle on the number 23 to indicate that 23 is included in the solutions.
- Shade all numbers to the left of 23 to show that [tex]\(x\)[/tex] can be any number less than or equal to 23.

With the inequality solved and understanding how to graph, you can identify the correct graph based on these characteristics.