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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.
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How do you graph a linear equation slope intercept?
You can graph a linear equation slope intercept by solving the equation and plugging in the numbers : y=mx+b
When solving a linear inequality do you always need to solve for y?
not always,sometimes you have to solve for x
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 does it mean when the result of solving a linear equation is x equals 0?
Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.
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 a literal equation differ from solving a linear equation?
Because linear equations are based on algebra equal to each other whereas literal equations are based on solving for one variable.
How does solving linear inequalities differ from solving linear equations?
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.
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.
Why do you clear decimals when solving a linear equation?
because you just do!
How do you graph a linear equation slope intercept?
You can graph a linear equation slope intercept by solving the equation and plugging in the numbers : y=mx+b
When solving a linear inequality do you always need to solve for y?
not always,sometimes you have to solve for x
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 equation for a linear inequality?
A linear inequalty may be of the form a1x1 + a2x2 + ... + anxn < bwhere the ai and b are constants and the xi are variables. The inequality symbol can be <, >, ≤ or ≥.
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.
What does it mean when the result of solving a linear equation is x equals 0?
Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.
