Solve Inequality 03D226

1. **State the problem:** We need to solve the inequality $$4x + 5 > 3$$ to find out for which values of $x$ this is true. 2. **Subtract 5 from both sides:** To isolate the term with $x$, subtract $5$ from both sides: $$4x + 5 - 5 > 3 - 5$$ This simplifies to: $$4x > -2$$ 3. **Divide both sides by 4:** Since $4$ is positive, dividing both sides by $4$ keeps the inequality direction the same: $$\frac{\cancel{4}x}{\cancel{4}} > \frac{-2}{4}$$ Simplifying: $$x > -\frac{1}{2}$$ 4. **Final answer:** The solution to the inequality is all $x$ values greater than $-\frac{1}{2}$. This means if you pick any number bigger than $-0.5$, the original inequality will be true.