Question

solve and write interval - notation for the solution set. then graph the solution set. 7x<4

a. the solution set is
type your answer in interval - notation. simplify your answer. use integers or fractions for any numbers in the expression.
b. there is no solution.
choose the correct graph below

Explanation:

Step1: Solve the inequality

Given $7x < 4$. Divide both sides by 7 to isolate $x$. We get $x<\frac{4}{7}$.

Step2: Write in interval - notation

The solution in interval - notation for $x <\frac{4}{7}$ is $(-\infty,\frac{4}{7})$.

Step3: Analyze the graph

The graph of $x <\frac{4}{7}$ is a number line with an open - circle at $\frac{4}{7}$ (since $x$ is strictly less than $\frac{4}{7}$) and an arrow pointing to the left.

Answer:

A. $(-\infty,\frac{4}{7})$
The correct graph is the one with an open - circle at $\frac{4}{7}$ (approx. 0.57) and an arrow pointing to the left. Without seeing the exact labels on the graphs in your options, the general form of the correct graph is a number line with an open - point at $\frac{4}{7}$ and the line extending to the left.