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December 20, 2014

December 20, 2014

Posted by **Tracy** on Sunday, January 23, 2011 at 2:02am.

-14is less then and equal to 3x -7less than and equal to -2

- math -
**MathMate**, Sunday, January 23, 2011 at 9:57amWrite

-14 <= 3x-7 <= -2

or

-14 ≤ 3x-7 ≤ -2

(≤ is written as "& l e ;" without the double quotes and without spaces).

There are two inequalities. We need to solve each one separately and find the solution interval that satisfies both inequalities.

-14 ≤ 3x-7

=> 3x-7 ≥ -14

=> 3x ≥ -14 + 7 = -7

=> x ≥ -7/3

3x-7 ≤ -2

=> 3x ≤ -2+7 = 5

=> x ≤ 5/3

Take the most restrictive interval to give

-7/3 ≤ x ≤ 5/3

Check the solution by substituting it back to the original inequalities.

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