Question

solve the linear inequality. other than \\( \varnothing \\), graph the solution set on a number line.\\( 5x < 5(x - 3) \\)\\( \dots \\)select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\( \bigcirc \\) a. the solution set in interval notation is \\( \square \\).\\( \quad \\) (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in\\( \quad \\) interval notation.)\\( \bigcirc \\) b. the solution set is \\( \varnothing \\).what is the graph of the solution set?\\( \bigcirc \\) a. \\( \quad \\) \\( \longleftarrow \frac{\quad}{-10} \frac{\quad}{0} \frac{\quad}{5} \frac{\quad}{10} \longrightarrow \\)\\( \bigcirc \\) b. \\( \quad \\) \\( \longleftarrow \frac{\quad}{-10} \frac{\quad}{0} \frac{\quad}{5} \frac{\quad}{10} \longrightarrow \\)\\( \bigcirc \\) c. \\( \quad \\) \\( \longleftarrow \frac{\quad}{-10} \frac{\quad}{0} \frac{\quad}{3} \frac{\quad}{5} \frac{\quad}{10} \longrightarrow \\)\\( \bigcirc \\) d. the solution set is \\( \varnothing \\).

Explanation:

Step1: Expand the right-hand side

$5x < 5x - 15$

Step2: Subtract $5x$ from both sides

$5x - 5x < 5x - 15 - 5x$
$0 < -15$

Step3: Evaluate the resulting statement

The inequality $0 < -15$ is false for all real numbers, so there is no solution.

Answer:

For the multiple-choice about the solution set:
B. The solution set is $\empty$.

For the graph of the solution set:
D. The solution set is $\empty$.