About Solving a Three-Part Inequality:
When we work with three-part linear inequalities, we find that we have three algebraic expressions separated by two inequality symbols. To find a solution, we are looking to isolate the variable in the middle. In other words, we want to find a solution where x is between two numbers.
Test Objectives
- Demonstrate the ability to solve a three-part inequality
- Demonstrate the ability to write a solution in interval notation
- Demonstrate the ability to graph an interval on the number line
#1:
Instructions: solve each, write in interval notation, graph.
$$a)\hspace{.2em}{-}28 ≤ 7x ≤ 63$$
$$b)\hspace{.2em}0 ≤ \frac{x}{3}< 2$$
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#2:
Instructions: solve each, write in interval notation, graph.
$$a)\hspace{.2em}3 ≤ 3 + x ≤ 1$$
$$b)\hspace{.2em}{-}15 < 3 - 3x ≤ 0$$
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#3:
Instructions: solve each, write in interval notation, graph.
$$a)\hspace{.2em}{-}14 ≤ 2x - 10 ≤ 10$$
$$b)\hspace{.2em}{-}46 < 4x - 10 < -6$$
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#4:
Instructions: solve each, write in interval notation, graph.
$$a)\hspace{.2em}{-}22 < -2 - 4x < 18$$
$$b)\hspace{.2em}23 ≤ 6x + 5 ≤ 53$$
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#5:
Instructions: solve each, write in interval notation, graph.
$$a)\hspace{.2em}64 ≤ -8x - 8 ≤ 72$$
$$b)\hspace{.2em}9 < 8 + x < 12$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}{-}4 ≤ x ≤ 9, [-4,9]$$
$$b)\hspace{.2em}0 ≤ x < 6, [0,6)$$
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#2:
Solutions:
$$a)\hspace{.2em}\text{No Solution}, \hspace{.2em}∅$$
$$b)\hspace{.2em}1 ≤ x < 6, [1,6)$$
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#3:
Solutions:
$$a)\hspace{.2em}{-}2 ≤ x ≤ 10, [-2, 10]$$
$$b)\hspace{.2em}{-}9 < x < 1, (-9, 1)$$
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#4:
Solutions:
$$a)\hspace{.2em}{-}5 < x < 5, (-5,5)$$
$$b)\hspace{.2em}3 ≤ x ≤ 8, [3,8]$$
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#5:
Solutions:
$$a)\hspace{.2em}{-}10 ≤ x ≤ -9, [-10,-9]$$
$$b)\hspace{.2em}1 < x < 4, (1,4)$$
