Question

1. write an expression that is equivalent to 2.5x + (-5y) - 2.5.

Explanation:

Step1: Simplify the sign of -5y

Recall that adding a negative is the same as subtracting, so \(2.5x + (-5y)-2.5\) can be rewritten as \(2.5x - 5y - 2.5\). Another equivalent form could be factoring out 2.5 from the first two terms: \(2.5(x - 2y)-2.5\) or factoring out 2.5 from all terms (though the constant term is -2.5, we can also write it as \(2.5x-5y - 2.5=2.5(x - 2y)-2.5\) or \(2.5x-5y-2.5=\frac{5}{2}x - 5y-\frac{5}{2}\) (converting decimals to fractions). Let's use factoring 2.5 from the first two terms:

Step1: Identify common factor

The coefficients of \(x\) and \(y\) are 2.5 and -5. Notice that -5 is \(2.5\times(- 2)\). So we can factor out 2.5 from the first two terms.

Step2: Factor out 2.5

\(2.5x+(-5y)-2.5 = 2.5x-5y - 2.5=2.5(x - 2y)-2.5\)

Or, if we want to write it without factoring, we can simplify the sign: \(2.5x-5y - 2.5\) is also equivalent.

Answer:

\(2.5x - 5y - 2.5\) (or \(2.5(x - 2y)-2.5\) or other equivalent forms)