Question

type the correct answer in the box.
simplify this expression:
4(1 - 3x) + 7x - 8.

Explanation:

Step1: Distribute the 4

We use the distributive property \(a(b + c)=ab+ac\) (here \(a = 4\), \(b=1\), \(c=- 3x\)) to expand \(4(1 - 3x)\). So we get \(4\times1-4\times3x=4 - 12x\).
The expression now becomes \(4-12x + 7x-8\).

Step2: Combine like terms (x - terms)

We combine the terms with \(x\): \(-12x+7x\). Using the rule \(ax+bx=(a + b)x\), here \(a=-12\), \(b = 7\), so \(-12x+7x=(-12 + 7)x=-5x\).
The expression is now \(4-5x - 8\).

Step3: Combine constant terms

We combine the constant terms \(4\) and \(-8\): \(4-8=-4\).
The simplified expression is \(-5x-4\).

Answer:

\(-5x - 4\)