Match the graph to the solution of the inequality. 2xlt 10 or (x)/(2)geqslant 3 o o

To solve the inequality \( 2x < 10 \) or \( \frac{x}{2} \geqslant 3 \), we will solve each part separately:<br /><br />1. **Solve \( 2x < 10 \):**<br /> Divide both sides by 2:<br /> \[<br /> x < 5<br /> \]<br /><br />2. **Solve \( \frac{x}{2} \geqslant 3 \):**<br /> Multiply both sides by 2:<br /> \[<br /> x \geqslant 6<br /> \]<br /><br />The solution to the inequality is the union of these two intervals because it uses "or." This means:<br />\[<br />x < 5 \quad \text{or} \quad x \geqslant 6<br />\]<br /><br />### Graph Representation:<br />- For \( x < 5 \), shade all values to the left of 5 (not including 5).<br />- For \( x \geqslant 6 \), shade all values to the right of 6 (including 6).<br /><br />The graph will show two separate regions: one shaded to the left of 5 with an open circle at 5, and another shaded to the right of 6 with a closed circle at 6.