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

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

Solution

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

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!