Solve the following inequality. 8-2xlt 4+3x Write your answer as an interval. Use INFTY for infty square I

To solve the inequality \(8 - 2x < 4 + 3x\), follow these steps:<br /><br />1. **Isolate the variable terms on one side:**<br /><br /> Start by subtracting \(3x\) from both sides:<br /> \[<br /> 8 - 2x - 3x < 4<br /> \]<br /> Simplify the left side:<br /> \[<br /> 8 - 5x < 4<br /> \]<br /><br />2. **Isolate the constant terms on the other side:**<br /><br /> Subtract 8 from both sides:<br /> \[<br /> -5x < 4 - 8<br /> \]<br /> Simplify the right side:<br /> \[<br /> -5x < -4<br /> \]<br /><br />3. **Solve for \(x\):**<br /><br /> Divide both sides by \(-5\). Remember, dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign:<br /> \[<br /> x > \frac{-4}{-5}<br /> \]<br /> Simplify:<br /> \[<br /> x > \frac{4}{5}<br /> \]<br /><br />The solution to the inequality is \(x > \frac{4}{5}\).<br /><br />In interval notation, this is expressed as:<br />\[<br />\left(\frac{4}{5}, \text{INFTY}\right)<br />\]