Question

simplify with addition and subtraction
which expression is equivalent to $(0.5x + 7) - (1.2x - 3)$?
\bigcirc $(0.5x + (-1.2x)) + (7 + (-3))$
\bigcirc $(0.5x + 1.2x) + (7 + (-3))$
\bigcirc $(0.5x + 1.2x) + (7 + 3)$
\bigcirc $(0.5x + (-1.2x)) + (7 + 3)$

Explanation:

Step1: Distribute the negative sign

To simplify \((0.5x + 7)-(1.2x - 3)\), we first distribute the negative sign to the terms inside the second parentheses. This gives us \(0.5x + 7 - 1.2x + 3\) (because subtracting a negative is adding a positive, so \(-(1.2x - 3)=-1.2x + 3\)).

Step2: Group like terms

Now, we group the \(x\)-terms and the constant terms. The \(x\)-terms are \(0.5x\) and \(-1.2x\), and the constant terms are \(7\) and \(3\). So we can write this as \((0.5x+(-1.2x))+(7 + 3)\).

Answer:

\((0.5x+(-1.2x))+(7 + 3)\) (the last option among the given choices)