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.
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.
