Question: Solve the linear inequality. Other than $\emptyset$, graph the solution set on a number line. \[…

Solve the linear inequality. Other than $\emptyset$, graph the solution set on a number line.

\[ 2x < 2(x - 6) \]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set in interval notation is $\boxed{\quad}$.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in interval notation.)

B. The solution set is $\emptyset$.

Solution

Step 1: Subtract \(2x\) from both sides. \[ 2x - 2x < 2(x - 6) - 2x \] Step 2: Simplify both sides. \[ 0 < -12 \] Since \(0\) is not less than \(-12\), there is no solution. The solution set is \(\varnothing\). Answer: B. The solution set is \(\varnothing\)