Question

solve the inequality and graph the solution.
4 + 3t < 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.
<--(-5)---(-4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->
submit

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( t \), we subtract 4 from both sides of the inequality \( 4 + 3t < 1 \). This gives us \( 4 + 3t - 4 < 1 - 4 \), which simplifies to \( 3t < -3 \).

Step2: Divide by 3

Next, we divide both sides of the inequality \( 3t < -3 \) by 3 to solve for \( t \). So, \( \frac{3t}{3} < \frac{-3}{3} \), which simplifies to \( t < -1 \).

For graphing the solution:

• The endpoint is at \( t = -1 \). Since the inequality is \( t < -1 \) (not \( t \leq -1 \)), we use an open circle at \( t = -1 \) to indicate that -1 is not included in the solution.
• Then, we draw a ray starting from the open circle at -1 and extending to the left (towards negative infinity) to represent all values of \( t \) that are less than -1.

Answer:

The solution to the inequality \( 4 + 3t < 1 \) is \( t < -1 \). When graphing, there is an open circle at \( -1 \) and a ray pointing to the left from \( -1 \).