vert t-2vert =5 4)) Click to select points on the number line.

## Step 1: Understand the Absolute Value Equation<br />### The equation given is $\vert t - 2 \vert = 5$. This means that the distance between $t$ and $2$ on the number line is $5$ units. Therefore, there are two possible cases for $t$: either $t - 2 = 5$ or $t - 2 = -5$.<br /><br />## Step 2: Solve Each Case Separately<br />### For the first case, $t - 2 = 5$, solve for $t$ by adding $2$ to both sides: <br />\[<br />t = 5 + 2 = 7<br />\]<br />### For the second case, $t - 2 = -5$, solve for $t$ by adding $2$ to both sides:<br />\[<br />t = -5 + 2 = -3<br />\]<br /><br />## Step 3: Identify the Points on the Number Line<br />### The solutions to the equation $\vert t - 2 \vert = 5$ are $t = 7$ and $t = -3$. These are the points on the number line where the condition of the absolute value equation is satisfied.