Questions: What is the solution set for the following inequality? 4x-3+6x>5x+7 x<2 x>0.8 x>2 x<0.8

What is the solution set for the following inequality? 4x-3+6x>5x+7 x<2 x>0.8 x>2 x<0.8
Transcript text: What is the solution set for the following inequality? \[ 4 x-3+6 x>5 x+7 \] $x<2$ $x>0.8$ $x>2$ $x<0.8$
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Solution

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Solution Steps

Step 1: Combine like terms to get the inequality into the form \(ax + b > cx + d\)

This step involves conceptual understanding of the problem form and does not require calculation.

Step 2: Subtract \(cx\) and \(d\) from both sides to get \(ax - cx > d - b\)

This simplifies the inequality by moving all terms involving \(x\) to one side and constants to the other.

Step 3: Simplify the inequality to \(x(a - c) > d - b\)

This step involves simplifying the inequality to isolate \(x\).

Step 4: Solve for \(x\) by dividing both sides by \(a - c\), resulting in \(x > \frac{d - b}{a - c}\) if \(a - c > 0\), or \(x < \frac{d - b}{a - c}\) if \(a - c < 0\).

If \(a - c = 0\), the inequality simplifies to a comparison of constants, which may result in a trivial truth or falsehood.

Final Answer: x > 2

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