1. The problem states that $|a + b| = a + b$ and $|b| = b$. We need to understand what these conditions imply about $a$ and $b$. 2. Recall the definition of absolute value: for any real number $x$, $|x| = x$ if $x \geq 0$, and $|x| = -x$ if $x < 0$. 3. From $|b| = b$, it follows that $b \geq 0$ because the absolute value of $b$ equals $b$ itself. 4. From $|a + b| = a + b$, it follows that $a + b \geq 0$. 5. Since $b \geq 0$, the inequality $a + b \geq 0$ implies $a \geq -b$. 6. Therefore, the conditions mean: - $b$ is non-negative. - $a$ is greater than or equal to $-b$. This is the solution set for $a$ and $b$ given the absolute value conditions.