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How does the solution to an inequality differ from the solution to an equation?
The solution to an inequality generally is a region with one more dimension. If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions. If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve. And so on, in higher dimensional spaces.
When graphing inequalities which inequality line is solid?
The line that includes whatever variables are included in the equation.
How are equations different from inequalities?
Equations are statements that state two expressions are equal, while inequalities are statements that state two expressions are not equal, meaning one is greater or less than the other. The graph of the solution set of an equation is a line or a curve, while the graph of the solution set of an inequality is a region at one side of the boundary line or curve obtained by supposing that the inequality was an equation.
What does a dashed boundary line indicate when graphing linear inequalities?
It means that the inequality is less than the value of the dashed line and is not equal to it.
What type of graph is used to represet an inequality?
For example, the solution set of x > 2 is the shaded portion of the number line to the right of 2 and a whole at 2. But in the xy-cordinate system is a shaded region to the right of the dashed vertical line that crosses the x-axis at 2. In the case of having a combination of two statements, an equation and an inequality, x ≥ 2, the whole will be filled in and the boundary line will be a full line.
When to use a solid line as a boundary when graphing a linear inequality?
If it is <= or >=
How do you know weather to shade above or below the line when graphing an inequality on the coordinate plane?
If the inequality has a > or ≥ sign, you shade above the line. If the inequality has a < or ≤ sign, you shade below it. Obviously, just an = is an equation, not an inequality.
When will the graph of an equation inequality be a dotted line?
The line is dotted when the inequality is a strict inequality, ie it is either "less than" (<) or "greater than" (>). If there is an equality in the inequality, ie "less than or equal to" (≤), "greater than or equal to" (≥) or "equal to" (=) then the line is drawn as a solid line.
What graph of linear is inequality 6x 2y -10?
The inequality (6x + 2y - 10 > 0) can be rewritten in slope-intercept form as (y > -3x + 5). The boundary line is (y = -3x + 5), which has a slope of -3 and a y-intercept of 5. The region above this line represents the solution set for the inequality. Since the inequality is strict (>), the boundary line itself is not included in the solution.
How does the solution to an inequality differ from the solution to an equation?
The solution to an inequality generally is a region with one more dimension. If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions. If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve. And so on, in higher dimensional spaces.
When graphing inequalities which inequality line is solid?
The line that includes whatever variables are included in the equation.
How are equations different from inequalities?
Equations are statements that state two expressions are equal, while inequalities are statements that state two expressions are not equal, meaning one is greater or less than the other. The graph of the solution set of an equation is a line or a curve, while the graph of the solution set of an inequality is a region at one side of the boundary line or curve obtained by supposing that the inequality was an equation.
Explain when to use a solid line as a boundary when graphing a linear inequality?
If the points that are ON the line satisfy the inequality then the line should be solid. Otherwise it should be dotted. Another way of putting that is, if the inequality is given in terms of ≤ or ≥, then use a solid line. If they are < or > use a dotted line.
When graphing a linear inequality what does a dashed boundary line inducarte?
The dashed boundary inducartes that the points on the boundary are not includedin the region which it bounds.This would be the case when the inequality says that one side is (more or less) than ...but not equal to ... the other side.
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.
When graphing inequalities where can solutions be found?
I think that you are asking about the linear inequalities with two variables, so my answer is related to them. First, you have to draw the boundary line (be careful, if your inequality does not contain the equal sign, the boundary line will be a dashed line, because the points on the line are not solutions to the inequality), which divide the coordinate system in two half-planes. Second, you have to test a point on either sides of the line (the best point is the origin, (0, 0), if it is not on the boundary line). If that point satisfies the inequality, then there are all its solutions, otherwise they are to the opposite side.
What does a dashed boundary line indicate when graphing linear inequalities?
It means that the inequality is less than the value of the dashed line and is not equal to it.
