Question

write an expression that is equivalent to $4.5d + 10 - 1.5d - 2.5$. which expression shows $4.5d + 10 - 1.5d - 2.5$ written as a sum? $4.5d + 10 + (-1.5d) + (-2.5)$ $4.5d + 10 + 1.5d + 2.5$

Explanation:

First Sub - Question (Write an equivalent expression)

Step1: Combine like terms for \(d\)

We have \(4.5d - 1.5d\). Using the rule of combining like terms \(ax+bx=(a - b)x\), here \(a = 4.5\), \(b=1.5\) and \(x = d\). So \(4.5d-1.5d=(4.5 - 1.5)d=3d\)

Step2: Combine constant terms

We have \(10-2.5 = 7.5\)

Step3: Combine the results

The equivalent expression is \(3d + 7.5\)

To write a subtraction as a sum, we use the rule that \(a - b=a+(-b)\). For the expression \(4.5d + 10-1.5d - 2.5\), we can rewrite \(- 1.5d\) as \(+(-1.5d)\) and \(-2.5\) as \(+(-2.5)\). So the expression becomes \(4.5d + 10+(-1.5d)+(-2.5)\)

Answer:

\(3d+7.5\)

Second Sub - Question (Write as a sum)