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Solve each compound inequality. Write the solution set in interval notation and graph.$$-8<t-8<8$$
The solution is (0,16)
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 7
Solving Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
McMaster University
Harvey Mudd College
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saw the compound inequality, right? The solution Set an interval notation and graph it. We have the compound inequality of negative eight is less than T minus eight is less than eight. To solve the compound inequality, we're going to use properties of inequalities toe isolate the variable by itself in the middle part of the inequality. So we need to get t all by itself between the two different inequality symbols. To do that, we're going to use inverse operations to undo any operation that's performed on T. Here we have team minus eight. So to undo the subtraction, we're going to add eight. Make sure we add eight to every part of the inequality. Negative eight plus eight is zero. Keep the inequality symbol less than T minus eight plus eight is T is less than eight plus eight is 16. So our solution set includes all the values that make the inequality. Zero is lesson T is less than 16. True, That's all values between zero and 16 but not including the two end points on our number line. We're gonna represent this with an open circle atter endpoints of zero in 16 and we're gonna shave the region between the two to include all those values that are between zero and 16 but not equal to zero and 16 an interval notation. We're going to use parentheses to open the interval that zero enclosed the interval at 16.
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