3. Find Y ° And C ° From The Following: Y=C+I_0+ - Gauthmath

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Question

Solve the following rational inequality and graph the solution set on a real number line. StartFraction x plus 3 Over x plus 4 EndFraction less than0 Question content area bottom Part 1 What is the solution set of the given inequality? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is enter your response here. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution set is empty setSHOW LESS0

Solution

The solution set is $$(-\infty, -4) \cup (-3, \infty)$$.

Step 1: Find the critical points by setting the numerator equal to zero: $$x+3=0$$ gives $$x=-3$$. Step 2: Find the critical points by setting the denominator equal to zero: $$x+4=0$$ gives $$x=-4$$. Step 3: Test the intervals $$(-\infty, -4)$$, $$(-4, -3)$$, and $$(-3, \infty)$$. Step 4: Choose $$x=-5$$ in $$(-\infty, -4)$$, which is negative. Step 5: Choose $$x=-3.5$$ in $$(-4, -3)$$, which is positive. Step 6: Choose $$x=0$$ in $$(-3, \infty)$$, which is negative.

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