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Solve for [tex]x[/tex]:

[tex]3 \frac{1}{2} \geq 1.4x[/tex]

Options:
A. [tex]x \geq 2 \frac{1}{2}[/tex]
B. [tex]x \leq 2 \frac{1}{2}[/tex]
C. [tex]x \geq 4 \frac{9}{10}[/tex]
D. [tex]x \leq 4 \frac{9}{10}[/tex]

Answer :

To solve the inequality [tex]\(3 \frac{1}{2} \geq 1.4x\)[/tex] and find the value of [tex]\(x\)[/tex], we follow these steps:

1. Convert the Mixed Number to a Decimal:
- The mixed number [tex]\(3 \frac{1}{2}\)[/tex] can be converted to a decimal.
- [tex]\(3 \frac{1}{2} = 3 + \frac{1}{2} = 3 + 0.5 = 3.5\)[/tex].

2. Set Up the Inequality:
- The inequality becomes:
[tex]\[
3.5 \geq 1.4x
\][/tex]

3. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], divide both sides of the inequality by 1.4:
[tex]\[
\frac{3.5}{1.4} \geq x
\][/tex]

4. Calculate the Division:
- Compute the left side:
[tex]\[
\frac{3.5}{1.4} = 2.5
\][/tex]

5. Rewrite the Inequality:
- Now, the inequality is:
[tex]\[
x \leq 2.5
\][/tex]

6. Interpret the Result:
- This means that the possible values for [tex]\(x\)[/tex] can be any number that is less than or equal to 2.5.
- In fraction form, [tex]\(2.5\)[/tex] is equivalent to [tex]\(2 \frac{1}{2}\)[/tex].

7. Conclusion:
- Thus, the correct solution to the inequality is:
[tex]\[
x \leq 2 \frac{1}{2}
\][/tex]

Therefore, the solution to the inequality [tex]\(3 \frac{1}{2} \geq 1.4x\)[/tex] is [tex]\(x \leq 2 \frac{1}{2}\)[/tex].

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