Question: Solve the linear inequality. Other than Ø, graph the solution set on a number line. \[ 5 -…

Solve the linear inequality. Other than Ø, graph the solution set on a number line.

\[ 5 - \frac{x}{4} > 7 \]

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 Ø.

Solution

Step 1: Subtract 5 from both sides of the inequality. \[ 5 - \frac{x}{4} - 5 > 7 - 5 \] This simplifies to: \[ - \frac{x}{4} > 2 \] Step 2: Multiply both sides by -4. Remember to reverse the inequality sign when multiplying by a negative number. \[ x < -8 \] Therefore, the solution set in interval notation is: \[ (-\infty, -8) \] The correct choice is: A. The solution set in interval notation: \((- \infty, -8)\)