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How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
Define solution of a linear inequality in two variable?
If the equal sign in a linear equation in two variables is replaced with an inequality symbol, the result is a linear inequality in two variables. 3x-2y>7 x<-5
How are linear inequalities different from linear equations?
A linear equation represents a line. A linear inequality represents part of the space on one side (or the other) of the line defined by the corresponding equation.
How is graphing a linear inequality in two variables different from graphing a linear equation in two variables?
Graphing a linear equation in two variables results in a straight line, representing all the solutions that satisfy the equation, while graphing a linear inequality produces a region on one side of the line that includes all the solutions satisfying the inequality. The line itself is solid if the inequality is ≤ or ≥, indicating that points on the line are included, or dashed if the inequality is < or >, indicating that points on the line are not included. Additionally, the area shaded represents all the combinations of values that satisfy the inequality, contrasting with the single line for an equation.
How is graphing a linear inequality different than graphing a linear equation?
In an inequality, you have to shade a side of a line to see show if the possible answers are greater than or equal to it
What is the difference between linear equations and linear inequalities?
It is easiest to describe the difference in terms of coordinate geometry. A linear equation defines a straight line in the coordinate plane. Every point on the line satisfies the equation and no other points do. For a linear inequality, first consider the corresponding linear equality (or equation). That defines a straight line which divides the plane into two. Depending on the direction of the inequality, all points on one side of the line or the other satisfy the equation, and no point from the other side of the line does. If it is a strict inequality (< or >) then points on the line itself are excluded while if the inequality is not strict (≤or ≥) then points on the line are included.
How do you solve a linear equation of an inequality or equation?
To solve a linear equation or inequality, first isolate the variable on one side of the equation or inequality. For an equation, use operations like addition, subtraction, multiplication, or division to simplify until the variable is alone (e.g., (ax + b = c) becomes (x = (c-b)/a)). For an inequality, follow similar steps but remember to reverse the inequality sign if you multiply or divide by a negative number. Finally, express the solution in interval notation or as a graph on a number line, depending on the context.
What do you mean by the term linear?
Linear means that the largest power(index) in the expression, equation, inequality etc, =1
How does solving linear inequality differ from solving linear equation?
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. The equation: x - 3 = 7 has one solution, that is x = 10. 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 value 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. The linear inequality x + 5 < 9 has as solution: x < 4. The solution set of this inequality is the interval (-infinity, 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. The open interval (1, 4) ; the 2 endpoints 1 and 4 are not included in the solution set. The closed interval [-2, 5] ; the 2 end points -2 and 5 are included. The half-closed interval [3, +infinity) ; the end point 3 is included.
How are linear equations and linear inequalities similar?
A linear equation corresponds to a line, and a linear inequality corresponds to a region bounded by a line. Consider the equation y = x-5. This could be graphed as a line going through (0,-5), (1,-4), (2,-3), and so on. The inequality y > x-5 would be the region above that line.
What is the graph of a linear inequality in two variables called?
A bivariate linear inequality.
Why are linear equation and linear inequalities not solved in the same manner?
Although there are similarities, the solutions to a linear equation comprise all points on one line: a one-dimensional object. The solutions to a linear inequality comprise all points on one side [or the other] of a line: a two-dimensional object.
