Question

solve the inequality 2/3 x < 5 which of the following graphs shows the solution

Answer 1

To solve the inequality \( \frac{2}{3} x < 5 \), we follow these steps:

1. Multiply both sides of the inequality by 3 to eliminate the fraction:
\[
3 \cdot \frac{2}{3} x < 3 \cdot 5
\]
simplifying to:
\[
2x < 15
\]

2. Next, divide both sides by 2:
\[
x < \frac{15}{2}
\]
which simplifies to:
\[
x < 7.5
\]

This means that the solution to the inequality is all values of \( x \) that are less than 7.5.

Now, when looking at the corresponding graph:
- The line will be drawn along the x-axis at \( x = 7.5 \).
- There will be an open circle at \( x = 7.5 \) (meaning 7.5 is not included in the solution).
- The shaded region will extend to the left of 7.5, indicating all values less than 7.5 are part of the solution.

Choose the graph that depicts these characteristics—an open circle at 7.5 with shading to the left.