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Linear Inequalities Test
About Solving Linear Inequalities in one Variable:

Solving a linear inequality in one variable is similar to solving a linear equation in one variable. Our goal is still to isolate the variable on one side, with a number on the other side. We must always remember to flip the inequality symbol when multiplying or dividing by a negative number.

Test Objectives:

•Demonstrate the ability to use the addition property of inequality

•Demonstrate the ability to use the multiplication property of inequality

•Demonstrate the ability to solve a linear inequality in one variable

Solving Linear Inequalities in one Variable Test:




#1:


Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.


a) -7(-5 + 4n) < -n - 5(n - 7)


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#2:


Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.


a) -3 - 5(2n + 9) < 9(-n - 5) - 12


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#3:


Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.


a) $$2n - \frac{5}{2}n < \frac{5}{3}n - \frac{13}{4}$$


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#4:


Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.


a) -28 ≤ 4n - 8 ≤ -20


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#5:


Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.


a) -49 ≤ -9a + 5 ≤ - 4


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Written Solutions:




#1:


Solution:


a) n > 0


(0, ∞)


graphing an interval on a number line


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#2:


Solution:


a) n > 9


(9, ∞)


graphing an interval on a number line


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#3:


Solution:


a) $$n > \frac{3}{2}$$


$$\left(\frac{3}{2},∞\right)$$


graphing an interval on a number line


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#4:


Solution:


a) -5 ≤ n ≤ -3


[-5,-3]


graphing an interval on a number line


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#5:


Solution:


a) 1 ≤ a ≤ 6


[1,6]


graphing an interval on a number line


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