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Can a linear equation and a linear inequality be solved in the same way? Explain why....

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yissy | Student, College Freshman | Honors

Posted September 17, 2012 at 3:16 PM via web

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Can a linear equation and a linear inequality be solved in the same way? Explain why. What makes them different?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 17, 2012 at 3:54 PM (Answer #1)

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You may use the same approach when you solve an equation or an inequality, but you need to interpret the results in different ways.

Considering a linear equation, you should always find the value of x that cancels the expression such that:

`ax + b = 0 => ax = -b => x = -b/a`

Considering the following linear inequality, you may perform the following steps such that:

`ax + b <= 0 => ax <= -b => x <= -b/a`

`ax + b>= 0 => ax>= -b => x>= -b/a`

Notice that you need to read the inequality `x <= -b/a` or `x>=-b/a`   in the following way: all values of x that are less or equal to value -`b/a` or all values of x that are larger or equal to -`b/a` .

Hence, you may use the same approach when you solve a linear equation of inequality, but the answers are different. The answer to a linear equation is a value x = -b/a , while the answer to a linear inequality is a range,`(-oo,-b/a], [-b/a,oo).`

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