Solving TwoStep Inequalities

1
Solving Two-Step Inequalities

• Lesson 7-6
• Calif. Standard
• Eric Bitter

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Example 1 Undoing OperationsSolve and graph
2y 3 5

• Determine what to undo first.
• Add 3 to each side.
• Simplify.
• Divide each side by 2.
• Simplify.

y is all numbers less than or equal to negative
one.
-3 -2 -1 0 1 2 3
3
Example 1b Undoing OperationsSolve and graph
5a 9 gt 11

• Determine what to undo first.
• Add 9 to each side.
• Simplify.
• Divide each side by 5.
• Simplify.

a is all numbers greater than four
1 2 3 4 5 6 7
Notice the hollow dot (four is not included)
4
Example 1c Undoing OperationsSolve and graph
17 lt 14

• Determine what to undo first.
• Subtract 17 to each side.
• Simplify.
• Multiply each side by 2.
• Simplify.
• c is all numbers less than negative six

-9 -8 -7 -6 -5 -4 -3
Notice the hollow dot (negative six is not
included)
5
Example 2 Two-Step InequalitiesSolve 9 gt
6

• Determine what to undo first.
• Subtract 6 to each side.
• Simplify.
• Multiply each side by -3.
• RULE Reverse the direction of the inequality
  when multiplying or dividing by a negative number.

6
Example 2b Two-Step InequalitiesSolve 4
7

• Determine...
• Subtract 4 to each side.
• Simplify.
• Multiply each side by -5.
• RULE Reverse the direction of the inequality
  when multiplying or dividing by a negative number.