Question

-3(4x - 8.2) < -11.98x + 14\frac{3}{4}
a. x < 49.25
b. x > 49.25
c. x < 492.5
d. x > 492.5

Explanation:

Step1: Expand the left side

First, we expand \(-3(4x - 8.2)\) using the distributive property \(a(b - c)=ab - ac\). So we get \(-3\times4x-(-3)\times8.2=-12x + 24.6\). The inequality becomes \(-12x + 24.6<-11.98x+14\frac{3}{4}\). We convert \(14\frac{3}{4}\) to a decimal, \(14\frac{3}{4}=14.75\). So the inequality is \(-12x + 24.6<-11.98x + 14.75\).

Step2: Move the x terms to one side

We add \(12x\) to both sides of the inequality to get all the \(x\) terms on one side. So we have \(-12x+12x + 24.6<-11.98x + 12x+14.75\), which simplifies to \(24.6 < 0.02x+14.75\).

Step3: Move the constant terms to the other side

Next, we subtract \(14.75\) from both sides. So \(24.6-14.75<0.02x+14.75 - 14.75\), which gives \(9.85<0.02x\).

Step4: Solve for x

To solve for \(x\), we divide both sides by \(0.02\). So \(\frac{9.85}{0.02} 492.5\).

Answer:

D. \(x>492.5\)