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Answer :
To solve the inequality [tex]\(4s + 6 \geq 6 + 4s\)[/tex], let's work through it step by step:
1. Write down the inequality:
[tex]\(4s + 6 \geq 6 + 4s\)[/tex]
2. Simplify the inequality:
We'll start by getting the terms involving the variable [tex]\(s\)[/tex] on one side. We can do this by subtracting [tex]\(4s\)[/tex] from both sides of the inequality:
[tex]\[
4s + 6 - 4s \geq 6 + 4s - 4s
\][/tex]
3. Simplify the terms:
This simplifies to:
[tex]\[
6 \geq 6
\][/tex]
4. Interpret the simplified inequality:
The statement [tex]\(6 \geq 6\)[/tex] is true, because 6 is equal to 6. Since there is no variable [tex]\(s\)[/tex] present in the inequality anymore, it means the original inequality holds true for any value of [tex]\(s\)[/tex].
5. Conclusion about the solution:
This means that the inequality [tex]\(4s + 6 \geq 6 + 4s\)[/tex] is always true, no matter what value [tex]\(s\)[/tex] takes. Therefore, the solution is that [tex]\(s\)[/tex] can be any real number.
6. Graphing the solution on a number line:
Since [tex]\(s\)[/tex] can be any real number, we graph this by shading the entire number line, indicating that all real numbers are solutions.
In summary, the inequality [tex]\(4s + 6 \geq 6 + 4s\)[/tex] is true for all real numbers [tex]\(s\)[/tex]. The solution to this inequality is that any real number can be a value for [tex]\(s\)[/tex].
1. Write down the inequality:
[tex]\(4s + 6 \geq 6 + 4s\)[/tex]
2. Simplify the inequality:
We'll start by getting the terms involving the variable [tex]\(s\)[/tex] on one side. We can do this by subtracting [tex]\(4s\)[/tex] from both sides of the inequality:
[tex]\[
4s + 6 - 4s \geq 6 + 4s - 4s
\][/tex]
3. Simplify the terms:
This simplifies to:
[tex]\[
6 \geq 6
\][/tex]
4. Interpret the simplified inequality:
The statement [tex]\(6 \geq 6\)[/tex] is true, because 6 is equal to 6. Since there is no variable [tex]\(s\)[/tex] present in the inequality anymore, it means the original inequality holds true for any value of [tex]\(s\)[/tex].
5. Conclusion about the solution:
This means that the inequality [tex]\(4s + 6 \geq 6 + 4s\)[/tex] is always true, no matter what value [tex]\(s\)[/tex] takes. Therefore, the solution is that [tex]\(s\)[/tex] can be any real number.
6. Graphing the solution on a number line:
Since [tex]\(s\)[/tex] can be any real number, we graph this by shading the entire number line, indicating that all real numbers are solutions.
In summary, the inequality [tex]\(4s + 6 \geq 6 + 4s\)[/tex] is true for all real numbers [tex]\(s\)[/tex]. The solution to this inequality is that any real number can be a value for [tex]\(s\)[/tex].
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