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

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

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
To determine the resulting inequality, we'll follow these steps methodically:

1. Start with the given inequality:
[tex]\[ -125 \geq -135 \][/tex]

2. Next, we are told to divide both sides of the inequality by -5. When dividing both sides of an inequality by a negative number, you must remember to reverse the direction of the inequality sign.

So, when we divide:
[tex]\[ \frac{-125}{-5} \quad \text{and} \quad \frac{-135}{-5}, \][/tex]
we get:
[tex]\[ 25 \quad \text{and} \quad 27 \][/tex]
respectively.

3. Therefore, the inequality sign flips:
[tex]\[ 25 \leq 27 \][/tex]

The resulting true inequality is:
[tex]\[ 25 \leq 27 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{25 \leq 27} \][/tex]
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