High School

What procedure can be used to solve the equation [tex]\frac{x}{19.3} = 38.6[/tex], and what is the solution?

A. Multiply [tex]\frac{x}{19.3}[/tex] by 19.3; the solution is 38.6.

B. Multiply [tex]\frac{x}{19.3}[/tex] by 19.3; the solution is 372.49.

C. Multiply both sides by 19.3; the solution is 38.6.

D. Multiply both sides by 19.3; the solution is 744.98.

Answer :

To solve the equation [tex]\(\frac{x}{19.3} = 38.6\)[/tex], we want to isolate [tex]\(x\)[/tex]. Here's how you can do it step-by-step:

1. Identify the operation: In the equation [tex]\(\frac{x}{19.3} = 38.6\)[/tex], [tex]\(x\)[/tex] is being divided by 19.3.

2. Remove the division: To isolate [tex]\(x\)[/tex], you need to do the opposite of dividing by 19.3, which is multiplying by 19.3.

3. Multiply both sides by 19.3:
[tex]\[
19.3 \times \frac{x}{19.3} = 38.6 \times 19.3
\][/tex]

4. Simplify the left side: The multiplication by 19.3 cancels out the division by 19.3 on the left side, leaving you with:
[tex]\[
x = 38.6 \times 19.3
\][/tex]

5. Calculate the right side: Multiply 38.6 by 19.3.
[tex]\[
x = 744.98
\][/tex]

So, the complete solution to the equation [tex]\(\frac{x}{19.3} = 38.6\)[/tex] is [tex]\(x = 744.98\)[/tex]. This matches the answer option: "Multiply both sides by 19.3, the solution is 744.98."