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The table below shows an inequality and a number by which to divide both sides.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Inequality & \begin{tabular}{c}
Divide each \\
side by
\end{tabular} \\
\hline
[tex]$-125 \geq -135$[/tex] & -5 \\
\hline
\end{tabular}
\][/tex]

What is the resulting true inequality?

A. [tex]$-25 \leq -27$[/tex]
B. [tex]$-25 \geq -27$[/tex]
C. [tex]$25 \geq 27$[/tex]
D. [tex]$25 \leq 27$[/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step.

1. Initial Inequality:
[tex]\[ -125 \geq -135 \][/tex]

2. Dividing Both Sides by -5:
When we divide or multiply an inequality by a negative number, we must reverse the inequality sign. Here, we are dividing both sides by -5.

3. Calculating the New Values:
[tex]\[ \frac{-125}{-5} \quad \text{and} \quad \frac{-135}{-5} \][/tex]

4. Simplifying Each Side:
[tex]\[ \frac{-125}{-5} = 25 \][/tex]
[tex]\[ \frac{-135}{-5} = 27 \][/tex]

5. Reversing the Inequality Sign:
Originally, we had \( \geq \), but since we are dividing by a negative number, the sign will reverse.
[tex]\[ 25 \leq 27 \][/tex]

6. Conclusion:
The resulting true inequality is:
[tex]\[ 25 \leq 27 \][/tex]

So, the final correct answer is:
[tex]\[ \boxed{25 \leq 27} \][/tex]
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