Consider the following compound inequality.\\ $\frac{18}{4} < \frac{y + 9}{2} < \frac{22}{4}$\\Step 2 of 2: Graph the solution set.
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For each compound inequality, give the solution set in both interval and graph form. See Examples $6-8$. $$ 3 x+2 \leq-7 \text { or }-2 x+1 \leq 9 $$
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For the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter $\mathrm{Y} 2=$ the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, liabs ( Find the points of intersection, recall $(2^{\text { nd }}$ CALC 5:intersection, lst curve, enter, } $2^{\text { nd }}$ curve, enter, guess, enter). Copy a sketch of the graph and shade the $x$ -axis for your solution set to the inequality. Write final answers in interval notation. $$ |x+2|-5 < 2 $$
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Select test values in each interval and substitute those values into the inequality. Note: If the test value makes the inequality true, then the entire interval is a solution to the inequality. If the test value makes the inequality false, then the entire interval is not a solution to the inequality. Use interval notation or set notation to write the final answer. Rational Inequality 1. Put the rational inequality in general form. where > can be replaced by <, ≤ and ≥. 2. Write the inequality into a single rational expression on the left side. (You can refer to the review section for solving unlike denominators) 3. Set the numerator and denominator equal to zero and solve. The values you get are called critical values. 4. Plot the critical values on a number line, breaking the number line into intervals. 5. Substitute critical values to the inequality to determine if the endpoints of the intervals in the solution should be included or not. 6. Select test values in each interval and substitute those values into the inequality. Note: If the test value makes the inequality true, then the entire interval is a solution to the inequality. If the test value makes the inequality false, then the entire interval is not a solution to the inequality. 7. Use interval notation or set notation to write the final answer. [-3, -1) ∪ [2, 4)
Kathleen C.
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