document.write( "Question 1084270: It is tempting to try to solve an inequality like an equation. For instance, we might try to solve 1<3/x
\n" ); document.write( "by multiplying both sides by x, to get x < 3, so the solution would be (-∞ ,3)
\n" ); document.write( "But that’s wrong; for example, x = -1 lies in this interval but does not satisfy the original inequality. Explain why this method does not work. In addition, solve the inequality correctly. Please be sure to explain your reasoning! \n" ); document.write( "

Algebra.Com's Answer #698363 by MathTherapy(10552) $\"\"$ $\"About$

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It is tempting to try to solve an inequality like an equation. For instance, we might try to solve 1<3/x
\n" ); document.write( "by multiplying both sides by x, to get x < 3, so the solution would be (-∞ ,3)
\n" ); document.write( "But that’s wrong; for example, x = -1 lies in this interval but does not satisfy the original inequality. Explain why this method does not work. In addition, solve the inequality correctly. Please be sure to explain your reasoning!
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When SOLVING INEQUALITIES, there are specific steps. One of the most important steps is to solve the inequality as you would, an equation.
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document.write( "Before doing any of that though you need to observe the fraction to the right of the INEQUALITY. It's . 
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document.write( "Right away, it's realized that x CANNOT = 0, or . The fact that  makes 0 a CRITICAL VALUE.
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document.write( "Solving the inequality the way you would an equation gives you a value of x = 3. Now, we have TWO (2) critical values, namely: 
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document.write( "Place these TWO (2) critical values on a NUMBER LINE and you'll notice that that are 3 intervals that MIGHT INCLUDE values for x: . 
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document.write( "You now use values WITHIN those INTERVALS to determine which values within which INTERVAL(S) satisfies(y) the INEQUALITY.\r
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document.write( "For x < 0, choose a value as such: one that's < 0. This VALUE WILL NOT satisfy the INEQUALITY.   
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document.write( "For 0 < x < 3, choose a value as such: one that's > 0 but < 3. This VALUE WILL satisfy the INEQUALITY.
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document.write( "For x > 0, choose a value as such: one that's > 0. This VALUE WILL NOT satisfy the INEQUALITY.\r
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document.write( "Therefore, only ONE (1) interval contains values that SATISFY the inequality:  \n" );
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