Some inequalities involve more than one operation. The best strategy to solve multi-step inequalities is to undo the operations in reverse order. In other words, work backward just as you did to solve multi-step equations. For example, 2x + 5 > 11 is a multi-step inequality. You can solve this inequality by following these steps.
1.
Solve 9 + 3x < 27. Check your solution.
Alternative Solutions:
Check: Substitute 0 and 6 into the
inequality.
The solution is {x│x <
6}.
Weather
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2. During Rafael’s trip to Mexico, the temperature was always warmer than 30º
Celsius. Use the formula 
, where F is degrees Fahrenheit and C is
degrees Celsius, to write and solve an inequality for the temperature in
degrees Farenheit.
Alternative Solutions:
Therefore,
Rafael can expect it to be warmer than 86°F in Mexico.
Remember to reverse the inequality symbol if you
multiply or divide by a negative number.
Example
3. Solve –4x + 3 ≥ 23 + 6x. Check
your solution.
Alternative Solutions:
The solution is {x│x ≤ –2}. Check your solution.
To solve inequalities that contain grouping symbols, you may
use the Distributive Property first.
Example
4.
Solve 8 ≤ –2(x – 5). Check your solution.
Alternative Solutions:
The solution is {x│x ≤ 1}. Check your solution.
You can use a graphing calculator to solve multi-step
inequalities.
Example
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5. Hannah’s scores on the first three of four 100-point tests were 85, 92,
and 90. What score must she receive on the fourth test to have a mean score of
more than 92 for all tests?
Alternative Solutions:
Sumber
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