Question

how many solution are there to the equation 5(x+10)-25=5x+25

Answer 1

Because this equation is has equal sides, and also has only 1 variable, you can test how many solutions it has by doing one where x is a negative number, and one where x is a positive number.
\[5(x+10)-25=5x+25\]
First I will do where x is positive. I will use x=3.
\[5(3+10)-25=5(3)+25\]
Now I will complete what is in parenthesis.
\[5(13)-25=5(3)+25\]
Now I will do the multiplication of both sides.
\[65-25=15+25\]
Now I will add and subtract on both sides.
\[40=40\]
So now that I know this equation works with the positive value of x, I will work out the equation with a negative value for x. First write the original equation.
\[5(x+10)-25=5x+25\]
Now replace x with the negative value. I will use x=-4.
\[5(-4+10)-25=5(-4)+25\]
Now work out the parentheses.
\[5(6)-25=5(-4)+25\]
Now multiply on both sides.
\[30-25=-20+25\]
Finally add and subtract on both sides.
\[5=5\]
Because this equation is true with both a positive value and a negative value for x, it means that this equation has an infinite number of solutions.

Answer 2

It reduces
5 (x + 10) - 25 = 5 x + 25
5 x +50 -25 =5x +25
0 x =0
Which is true for any x