Question

solve for t and graph the solution. 17t + 5 ≤ 9t + 5 or - 11t - 9 > - 13t + 3. plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Solve the first inequality

Solve $17t + 5\leq9t + 5$.
Subtract $9t$ from both sides: $17t-9t + 5\leq9t-9t + 5$, which simplifies to $8t+5\leq5$.
Subtract 5 from both sides: $8t+5 - 5\leq5 - 5$, getting $8t\leq0$.
Divide both sides by 8: $t\leq0$.

Step2: Solve the second inequality

Solve $-11t - 9>-13t + 3$.
Add $13t$ to both sides: $-11t+13t - 9>-13t+13t + 3$, which simplifies to $2t-9>3$.
Add 9 to both sides: $2t-9 + 9>3 + 9$, getting $2t>12$.
Divide both sides by 2: $t > 6$.

Step3: Graph the solutions

For $t\leq0$, we have a ray starting from 0 and going to the left on the number - line, with a closed - circle at 0 (since it is $\leq$).
For $t>6$, we have a ray starting from 6 and going to the right on the number - line, with an open - circle at 6 (since it is $>$).

Answer:

The solution is $t\leq0$ or $t > 6$. On the number - line, for $t\leq0$, we have a ray starting from 0 and going left with a closed - circle at 0. For $t>6$, we have a ray starting from 6 and going right with an open - circle at 6.