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