Question
Multiply by the reciprocal of the coefficient of x on both sides of \( 5 \mathrm{x}=-10 \). \( \frac{1}{5} \cdot 5 \mathrm{x}=\square \cdot-10 \)
Ask by Turner Smith. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
-2
\]
Solution
To solve the equation \( 5x = -10 \) by multiplying both sides by the reciprocal of the coefficient of \( x \), we first identify the coefficient of \( x \), which is \( 5 \). The reciprocal of \( 5 \) is \( \frac{1}{5} \).
Now, we can multiply both sides of the equation by \( \frac{1}{5} \):
\[
\frac{1}{5} \cdot 5x = \frac{1}{5} \cdot -10
\]
Now, let's simplify both sides:
1. On the left side:
\[
\frac{1}{5} \cdot 5x = x
\]
2. On the right side:
\[
\frac{1}{5} \cdot -10 = -2
\]
Putting it all together, we have:
\[
x = -2
\]
Thus, the equation becomes:
\[
\frac{1}{5} \cdot 5x = -2
\]
So, the answer to fill in the square is:
\[
-2
\]
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Simplify this solution Bonus Knowledge
Let's break it down in a fun way! When we multiply both sides of the equation \( 5 x = -10 \) by the reciprocal of the coefficient of \( x \), which is \( \frac{1}{5} \), we simplify the left side. It’s like waving a magic wand and poof! The \( 5 \) cancels out with \( \frac{1}{5} \), leaving us with \( x \). Now, on the right side, we multiply \( \frac{1}{5} \) by \(-10\). Since we're just a step away from revealing the value of \( x \), this means we need to compute that part: \(-10 \times \frac{1}{5} = -2\). So now we have: \[ x = -2 \] And just like that, we land at our solution! Feel free to let me know if you want to explore more fun math concepts!
