1. The first problem is to solve the inequality $2x + 1 \geq 5$. 2. Start by isolating $x$ on one side. Subtract 1 from both sides: $$2x + \cancel{1} - \cancel{1} \geq 5 - 1$$ $$2x \geq 4$$ 3. Now divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} \geq \frac{4}{2}$$ $$x \geq 2$$ 4. This means the solution set is all $x$ such that $x$ is greater than or equal to 2. 5. To check, substitute $x=2$ into the original inequality: $$2(2) + 1 = 4 + 1 = 5$$ which satisfies $\geq 5$. 6. For $x=3$: $$2(3) + 1 = 6 + 1 = 7 \geq 5$$ which is true. 7. Therefore, the solution $x \geq 2$ is correct. Since you asked if you worked these out right, the first problem's solution is correct. "slug":"inequality solution","subject":"algebra","desmos":{"latex":"y=2x+1","features":{"intercepts":true,"extrema":true}},"q_count":1