Question

station 4: schoology staar practice
which expression is equivalent to $1.5(4j - 10k) - 2.5(8j + 6k)$?
$\circ -26j$
$\circ -14j$
$\circ -14j - 30k$
$\circ -12j + 4k$

Explanation:

Step1: Distribute the coefficients

First, 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, combine the \(j\) terms and the \(k\) terms separately.
For the \(j\) terms: \(6j - 20j = (6 - 20)j = -14j\).
For the \(k\) terms: \(-15k - 15k = (-15 - 15)k = -30k\).
Putting them together, the expression simplifies to \(-14j - 30k\).

Answer:

\(-14j - 30k\) (corresponding to the option with \(-14j - 30k\))