The Techniques For Solving Linear Equations And Linear Inequalities Are Similar, Yet Different. Can You Explain And Give An Example Of Both A Linear Equation And A Linear Inequality That Demonstrates This Difference?

A typical linear equation in one variable might be ax+b=0. In similar fashion a typical linear inequality might be ax+b<0. The solution to the equation is found by subtracting "b" from both sides, then dividing both sides by "a" so that x = -b/a. The same method works the same way for the inequality if "a" is positive. That is, x < -b/a. However, if "a" is negative, the direction of the inequality must be reversed: X > -b/a.

Example: 2x-6=0 has solution x=-(-6)/2 = 3. 2x-6<0 has solution x<3.
Example showing the difference: -2x-6=0 has solution x=-3. -2x-6<0 has solution x > -(-6)/(-2), or x>-3.

When working with equations or inequalities, you can add or subtract the same thing from both sides without any problem. When working with equations or inequalities, you can multiply or divide both sides by any positive number without any problem. When working with equations, you can multiply or divide both sides by any negative number without any problem, but when you multiply or divide both sides of an inequality by some negative number, you need to reverse the sense of the inequality.

Linear equations are the equations with the highest variable power one. Linear equations are equations of straight line and when we say the solution of linear equations it means to find the relation between the lines. If the lines are parallel they will not intersect while if they are not parallel then they will intersect at a point and the point can be found by solving them simultaneously. They can be solved by substitution, comparison method and equating the coefficients of variable.
Linear inequalities can be solved by making the equation of given inequalities by replacing equality sign by sign of inequality. The point of intersection is found out by the simple method of solving the linear equations. Then the points are put in original inequalities and test which point satisfies the inequality.
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