Answer:
To find expressions that are equivalent to \(10a - 25 + 5b\), we can simplify the expression using basic algebraic operations.
First, we can group the terms that have the same variable together. In this case, we have terms with \(a\) and terms with \(b\):
\(10a - 25 + 5b\)
Next, we can combine like terms. The terms \(10a\) and \(-25\) are constants because they don't have any variables attached to them. So, we can add or subtract them directly:
\(10a - 25 + 5b = (10a + 5b) - 25\)
Now, let's consider the answer choices to find equivalent expressions:
1. \(10(a - 2.5) + 5b\) - This expression is not equivalent to the original expression because it includes a factor of 10 multiplying the expression inside the parentheses, which changes the value of the entire expression.
2. \(10a - 5b - 25\) - This expression is equivalent to the original expression because the terms \(10a\) and \(5b\) are in the same order and have the same coefficients, and the constant term \(-25\) remains unchanged.
3. \(-5b + 10a - 25\) - This expression is also equivalent to the original expression because the terms are rearranged but still have the same coefficients and constant term.
So, the expressions that are equivalent to \(10a - 25 + 5b\) are \(10a - 5b - 25\) and \(-5b + 10a - 25\).
Explanation: