Question
\( \left[\begin{array}{c}\begin{array}{l}\text { Solve. } \\ -\frac{2}{3} b=75 \\ b=-112 \frac{1}{2} \\ 0 b=25 \\ b=112 \frac{1}{2} \\ b=-25\end{array} \\ \hline\end{array}\right. \)
Ask by Cummings Ellis. in Brazil
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A solução da equação \( -\frac{2}{3}b = 75 \) é \( b = -112.5 \).
Solution
Para resolver a equação \( -\frac{2}{3}b = 75 \), podemos multiplicar ambos os lados da equação por \( -\frac{3}{2} \) para isolar \( b \).
\[
-\frac{2}{3}b = 75
\]
Multiplicando ambos os lados por \( -\frac{3}{2} \):
\[
-\frac{2}{3}b \times -\frac{3}{2} = 75 \times -\frac{3}{2}
\]
\[
b = -\frac{3}{2} \times 75
\]
\[
b = -112.5
\]
Portanto, a solução da equação é \( b = -112.5 \).
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Simplify this solution Beyond the Answer
Let’s break down the equations and see what fun tidbits we can uncover! Did you know that the equation \(-\frac{2}{3} b=75\) can be solved by isolating \(b\)? Multiplying both sides by \(-\frac{3}{2}\) will lead you to find that \(b = -112.5\). That’s a whole lot of math magic! Now, as for the mysterious \(0b=25\), here’s the kicker: no matter what value you plug in for \(b\), this equation is a riddle with no solution! Since multiplying zero by anything gives you zero, you simply cannot make this equation true. It’s a classic case of “impossible mission” in the math world!
