Solve for r and graph the solution. 4+19rgeqslant 17r-6geqslant -10+19r

## Step 1<br />The given inequality is \(4 + 19r \geq 17r - 6 \geq -10 + 19r\). This inequality can be broken down into two separate inequalities: \(4 + 19r \geq 17r - 6\) and \(17r - 6 \geq -10 + 19r\).<br /><br />## Step 2<br />Let's start with the first inequality \(4 + 19r \geq 17r - 6\). To isolate \(r\), we subtract \(17r\) from both sides, which gives us \(2r \geq -10\).<br /><br />## Step 3<br />Next, we divide both sides by 2 to solve for \(r\), which gives us \(r \geq -5\).<br /><br />## Step 4<br />Now, let's solve the second inequality \(17r - 6 \geq -10 + 19r\). To isolate \(r\), we subtract \(17r\) from both sides, which gives us \(-2r \geq -4\).<br /><br />## Step 5<br />Finally, we divide both sides by -2 to solve for \(r\), which gives us \(r \leq 2\).<br /><br />## Step 6<br />The solution to the original inequality is the intersection of the solutions to the two inequalities. This means that \(r\) must satisfy both \(r \geq -5\) and \(r \leq 2\). Therefore, the solution to the original inequality is \(-5 \leq r \leq 2\).