I just needed a fast answer to "Explain why a linear equasion and a linear inequality can or can't be solved the same way. What makes them different?

Question

I'm trying to understand the question myself, this is my third attempt at Algebra 1, I suck in Math, I'm 58, and need Math 208 and 209 to get my degree or I don't get one.  So I'm in my 2nd week right now  I haven't a clue what it means.

 

Answer 1

To add on to the explanation above...when we have an inequality, this is a much looser constraint than an equality...

 

Consider a graphical interpretation of the following:

 

y = 2x+1

 

y > x-2

 

Both look like linear expressions y ? mx+b....however when we graph the set of points (x,y) in each case, the regions look quite different... y=2x+1 is a line, the solutions to the equation are all the points that lie on the line of slope 2 with y-intercept 1...y > x-2 is a region bounded by the line y=x-2, where all the points we consider to be solutions to the inequality lie ABOVE the line.

 

This graphical approach to interpreting solutions of equations and inequalities can help you to understand the similarities and differences between finding solutions to equalities and inequalities.

 

In more general terms, solving an equation leads to less solutions than solving the exact same inequality will...this fact has to do with the dimension of the solution space.

 

Hope this helps!

Answer 2

One difference is the number of solutions:

 

Linear equation: x = 5, only one solution, 5.

Linear inequality x > 5, a whole lot a solutions, everything more than 5.

 

Another difference is when multiplying or dividing by a negative number.

 

- x = -5, when both sides are multiplied by -1

x = 5, nothing happens to the equal sign.

 

- x > - 5, when both sides are multiplied by -1

x < 5, the direction of the inequality changes.

 

Ask if you need more information.