What kind of Inequality Is this? vert x-2vert lt 7 AND cor compound inquality OR compound inequality

To solve the inequality $\vert x-2\vert \lt 7$, we need to consider the definition of absolute value. The absolute value of a number is the distance of that number from zero on the number line. In this case, the absolute value of $(x-2)$ represents the distance of $x$ from 2 on the number line.<br /><br />The inequality $\vert x-2\vert \lt 7$ means that the distance of $x$ from 2 is less than 7. This can be written as a compound inequality:<br /><br />$-7 < x-2 < 7$<br /><br />To solve this compound inequality, we need to isolate $x$ by adding 2 to all parts of the inequality:<br /><br />$-7 + 2 < x < 7 + 2$<br /><br />Simplifying, we get:<br /><br />$-5 < x < 9$<br /><br />Therefore, the solution to the inequality $\vert x-2\vert \lt 7$ is the compound inequality $-5 < x < 9$.