to determine whether a given number is a solution of an equation.

Problem:
Is 5 a solution of 10x-xto the 2nd power = 3x-10?
my work: 10(5)-25=25 and 50-25=25 so x is not a solution. right or wrong? Im new at this

10x - x^2 = 3x - 10

50 - 25 ≠ 15 - 10

You are right.

To determine whether a given number is a solution of an equation, you need to substitute the value of the variable in the equation and check if both sides of the equation are equal.

In this case, you have the equation 10x - x^2 = 3x - 10 and you want to check if x = 5 is a solution.

To do this, substitute x = 5 into the equation:
10(5) - 5^2 = 3(5) - 10

Now, simplify both sides of the equation:
50 - 25 = 15 - 10

50 - 25 equals 25 and 15 - 10 equals 5, so the equation becomes:
25 = 5

Since 25 does not equal 5, we can conclude that x = 5 is not a solution to the equation.

Therefore, your work is incorrect. The correct conclusion is that x = 5 is not a solution to the equation. Keep practicing and you'll get the hang of it!