Solve the equation in part
9.75p+10=9.35p+20
Explain how you solved the equation and what the solution represents. Can you start with a different first step?
To solve the equation, we will first rearrange it by moving the constant terms to one side of the equation and the variable terms to the other side.
9.75p + 10 = 9.35p + 20
Subtracting 9.35p from both sides:
9.75p - 9.35p + 10 = 9.35p - 9.35p + 20
0.4p + 10 = 20
Subtracting 10 from both sides:
0.4p + 10 - 10 = 20 - 10
0.4p = 10
To isolate the variable p, we divide both sides of the equation by 0.4:
(0.4p) / 0.4 = 10 / 0.4
p = 25
Therefore, the solution to the equation is p = 25. This means that when p is equal to 25, the equation is satisfied.
Starting with a different first step:
Instead of rearranging the equation and moving terms, we can start by subtracting 9.35p from both sides:
9.75p + 10 - 9.35p = 9.35p + 20 - 9.35p
0.4p + 10 = 20
Continuing with the same steps as before:
0.4p + 10 - 10 = 20 - 10
0.4p = 10
(0.4p) / 0.4 = 10 / 0.4
p = 25
Regardless of the starting step, we reach the solution p = 25. This value represents the value of p that makes the equation true.