Solve for \( x \) and graph the solution on the number line below. \[ x+7 \geq 5 \]

To solve the inequality \( x + 7 \geq 5 \), we first want to isolate \( x \). We can do this by subtracting 7 from both sides of the inequality: \[ x + 7 - 7 \geq 5 - 7 \] This simplifies to: \[ x \geq -2 \] Now, to graph this on the number line, you would place a closed dot at -2 (indicating that -2 is included in the solution) and shade to the right, showing that all numbers greater than -2 are included in the solution. Now, if you're looking for extra clarity, inequalities like this often show up in real-life scenarios, such as determining minimum values required for grades or budgets. You can think of this as finding out that if you want to score at least a 5 after accounting for points you’ve already won (7), you need to ensure your base score (x) is at least -2. Also, be sure to avoid common mistakes like flipping the inequality sign when adding or subtracting; this happens only when multiplying or dividing by a negative number! Keep practicing, and soon you'll become a pro at solving inequalities!