Question

which expression is equivalent to $1.5(4j - 10k) - 2.5(8j + 6k)$?
a $-12j + 4k$
b $-26j$
c $-14j - 30k$
d $-14j$

Explanation:

Step1: Distribute the coefficients

First, we distribute \(1.5\) to \(4j - 10k\) and \(-2.5\) to \(8j + 6k\).
For \(1.5(4j - 10k)\), we have \(1.5\times4j - 1.5\times10k = 6j - 15k\).
For \(-2.5(8j + 6k)\), we have \(-2.5\times8j - 2.5\times6k = -20j - 15k\).

Step2: Combine like terms

Now we combine the \(j\) terms and the \(k\) terms separately.
The \(j\) terms are \(6j - 20j = -14j\).
The \(k\) terms are \(-15k - 15k = -30k\).
So the simplified expression is \(-14j - 30k\).

Answer:

C. \(-14j - 30k\)