Solve and graph the solution set. \( -\frac{3}{4} x \geq-\frac{11}{12}+\frac{1}{3} x \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type your answer in interval notation.) B. There is no solution.
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To solve the inequality, first, we need to isolate \( x \). Start by getting all terms involving \( x \) on one side and constants on the other: 1. Rewrite the inequality: \[ -\frac{3}{4} x + \frac{1}{3} x \geq -\frac{11}{12} \] 2. Find a common denominator for the \( x \) terms, which is 12: \[ -\frac{9}{12} x + \frac{4}{12} x \geq -\frac{11}{12} \] 3. Combine the \( x \) terms: \[ -\frac{5}{12} x \geq -\frac{11}{12} \] 4. Multiply both sides by -12/5 (remember to reverse the inequality because you are multiplying by a negative): \[ x \leq \frac{11}{5} \] The solution set in interval notation is: \[ (-\infty, \frac{11}{5}] \] Now, for the graph of the solution set, you would shade everything to the left of and including \( \frac{11}{5} \) on a number line. You would mark \( \frac{11}{5} \) with a solid dot to indicate that it is included in the solution set.
