Question

4 what operation can you use on both sides of the equation $100 = 100 \div y$ to solve the equation for $y$? solve the equation for $y$. then explain how to check the solution.

Explanation:

Step1: Identify the operation

To isolate \( y \), we can multiply both sides of the equation \( 100 = \frac{100}{y} \) by \( y \) to get rid of the denominator on the right - hand side.
\[100\times y=\frac{100}{y}\times y\]
Simplifying the right - hand side, we have \( 100y = 100 \).

Step2: Solve for \( y \)

Now, divide both sides of the equation \( 100y=100 \) by 100.
\[\frac{100y}{100}=\frac{100}{100}\]
Which gives us \( y = 1 \).

Step3: Check the solution

To check the solution, substitute \( y = 1 \) back into the original equation \( 100=\frac{100}{y} \).
Left - hand side: \( 100 \)
Right - hand side: \( \frac{100}{1}=100 \)
Since the left - hand side is equal to the right - hand side when \( y = 1 \), the solution is correct.

Answer:

The operation is multiplying both sides by \( y \) (and then dividing by 100). The solution of the equation \( 100=\frac{100}{y} \) is \( y = 1 \). To check, substitute \( y = 1 \) into the original equation, and both sides equal 100.