```ts
export function mergeIntervals(intervals: number[][]): number[][] {
  if (!intervals.every(([start, end]) => start <= end)) {
    throw new Error("Invalid interval: end must be greater than or equal to start.");
  }

  intervals.sort((a, b) => a[0] - b[0]);

  const mergedIntervals: number[][] = [];
  let currentInterval = intervals[0];

  for (let i = 1; i < intervals.length; i++) {
    const [start, end] = intervals[i];
    if (end > currentInterval[1]) {
      mergedIntervals.push(currentInterval);
      currentInterval = { start, end };
    } else if (end >= currentInterval[0]) {
      currentInterval.end = Math.max(currentInterval.end, end);
    }
  }

  mergedIntervals.push(currentInterval);

  return mergedIntervals;
}
```