How does solving linear inequalities differ from solving linear equations?

Answer 1

Linear inequalities are equations, but instead of an equal sign, it has either a greater than, greater than or equal to, less than, or a less than or equal to sign. Both can be graphed.

Solving linear equations mainly differs from solving linear inequalities in the form of the solution.

1. Linear equation.

For each linear equation in x, there is only one value of x (solution) that makes the equation true.

Example 1. The equation: x - 3 = 7 has one solution, that is x = 10.

Example 2. The equation: 3x + 4 = 13 has one solution that is x = 3.

2. Linear inequality.

On the contrary, a linear inequality has an infinity of solutions, meaning there is an infinity of values of x that make the inequality true. All these x values constitute the "solution set" of the inequality. The answers of a linear inequality are expressed in the form of intervals.

Example 3. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 4)

Example 4. The inequality 4x - 3 > 5 has as solution x > 2. The solution set is the interval (2, +infinity).

The intervals can be open, closed, and half closed.

Example: The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set.

Example: The closed interval [-2, 5] ; the 2 end points -2 and 5 are included.

Example : The half-closed interval [3, +infinity) ; the end point 3 is included.