Questions: What is the value of x in the linear inequality? -3(4x-8.2) < -11.98x + 14 3/4 A. x<49.25 B. x>49.25 C. x<492.5 D. x>492.5

Transcript text: Formula Sheet What is the value of $x$ in the linear inequality? \[ -3(4 x-8.2)<-11.98 x+14 \frac{3}{4} \] A. $x<49.25$ B. $x>49.25$ C. $x<492.5$ D. $x>492.5$

Solution

Solution Steps

Step 1: Distributing and Rearranging the Inequality

We start with the inequality: \[ -3(4x - 8.2) < -11.98x + 14 \frac{3}{4} \] Distributing $-3$ gives: \[ -12x + 24.6 < -11.98x + 14.75 \]

Step 2: Combining Like Terms

Next, we rearrange the inequality to isolate $x$: \[ -12x + 11.98x < 14.75 - 24.6 \] This simplifies to: \[ -0.02x < -9.85 \]

Step 3: Isolating $x$

Dividing both sides by $-0.02$ (and reversing the inequality sign) yields: \[ x > 492.5 \]

Final Answer

The solution to the inequality is: \[ \boxed{x > 492.5} \]

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