Download MA.8.A.4.2 Solve and graph one

MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
An inequality is a mathematical sentence that contains > or < to compare or describe a range of values. Some
inequalities use the symbols ≤ or ≥. The symbol ≤ is read is less than or equal to. The symbol ≥ is read is
greater than or equal to.
Inequalities can be graphed on a number line. An open or closed dot is used to indicate where they begin. An
arrow to the left or to the right is used to show that they continue in the indicated direction. An open circle is
used with inequalities having < or >. A closed circle is used with inequalities having ≤ or ≥.
Example: d  2
Draw a number line. Place a closed circle on -2, draw a line and an arrow to the left.
Example: d  2
Draw a number line. Place an open circle on 2, draw a line and an arrow to the right.
To solve inequalities, use inverse operations to undo each operation in reverse order of the order of operations.
(**When you multiply or divide by a negative number remember to switch the inequality sign)
One-Step Inequalities
Examples: Solve the inequality. Graph the solution set on a number line.
1. 9  r  5
Write the inequality
2. x  7  4
Write the inequality
5
5
7 7
Subtraction Property of Inequality
Addition Property of Inequality
x3
Simplify
Simplify
4  r or r  4
Graph the solution set.
Graph the solution set.
3.
t
 3
7
Write the inequality
t
 7  3 7 Multiplication Property of Inequality
7
t  21
Simplify
Graph the solution set.
4. 4 x  32
Write the inequality
4 x 32
Division Property of Inequality

4
4
x8
Simplify
Graph the solution set.
Two-Step Inequalities
Example: Solve 4 x  2  18 . Graph the solution set on a number line.
4 x  2  18
Write the inequality.
Addition Property of Inequality
2 2
4x
 20
Simplify.
4x
20
Division Property of Inequality

4
4
x5
Simplify.
Graph the solution set.
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MA.8.A.4.2 Practice Problems
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21.
22.
23.
24. Randall is raking leaves to save money for a vacation. He charges $12 per yard. Randall
already has $40 and wants to have at least $148 to take with him. Write and solve an inequality
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to determine how many yards Randall needs to rake to have at least $148. Interpret the solution.
25. Solve the following inequality for x: 6x-3> 10. Graph the solution set.
26. A rental company charges $15 plus $4 per hour to rent a moped. If Billy does not want to
spend more than $27 for his rental, write and solve an inequality to find how many hours he can
rent the moped and not spend more than $27. Interpret the solution.
27.
10 
28.
x
6
3
30.
29.
31.
 6  4  2 x
 15  5b  10
x
1  5
2
33.
32.
 6  2c  2
12  d  3  13
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