Question

solve the inequality and graph the solution.
1 ≥ (t/3) - 1
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
number line with ticks at -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( t \), we add 1 to both sides of the inequality \( 1 \geq \frac{t}{3} - 1 \). This gives \( 1 + 1 \geq \frac{t}{3} - 1 + 1 \), which simplifies to \( 2 \geq \frac{t}{3} \).

Step2: Multiply both sides by 3

To solve for \( t \), we multiply both sides of the inequality \( 2 \geq \frac{t}{3} \) by 3. This gives \( 2 \times 3 \geq \frac{t}{3} \times 3 \), which simplifies to \( 6 \geq t \) or \( t \leq 6 \).

Answer:

The solution to the inequality is \( t \leq 6 \). To graph this, we plot a closed circle at \( 6 \) (since the inequality is "less than or equal to") and draw a ray to the left of \( 6 \) on the number line.