How do you know if an inequality is shade above or shade below?
How do you know if an inequality is shade above or shade below?
Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
Why do we shade when graphing inequalities?
We shade below (not above) because y is less than (or equal to) the other side of the inequality. We draw a solid line (not dashed) because we’re dealing with an “or equal to” inequality. The solid line indicates that points on the line are solutions to the inequality.
How do you know if your inequality is solid or dashed?
To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
How do you know which side to shade when graphing inequalities?
Shade the top side of the boundary line if you have the inequality symbols > or ≥. Shade the bottom side of the boundary line if you have the inequality symbols < or ≤.
How do you shade systems of inequalities?
There are three steps:
- Rearrange the equation so “y” is on the left and everything else on the right.
- Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
- Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).
What is it called when my shaded areas do not overlap?
Inequality 1 is graphed in blue and inequality 2 is graphed in red. The overlap of the shaded regions (purple shading) represents the solution. Inequality 1 is graphed in blue and inequality 2 is graphed in red. In this case the regions do not overlap. This indicates that there is no solution to the system.
Is it possible for a quadratic inequality not to have a real solution?
Whenever you have a quadratic inequality where the associated quadratic equation does not have real solutions (that is, where the associated parabola does not cross the x-axis), the solution to the inequality will either be “all x” or “no x”, depending upon whether the parabola is on the side of the axis that you need.
Which compound inequality has no solution?
Here are the steps to follow when solving absolute value inequalities: Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
How do you know if a compound inequality is all real numbers?
Solve each inequality separately. The inequality sign is reversed with division by a negative number. Since y could be less than 3 or greater than or equal to −4, y could be any number. The solution is all real numbers.
How do you know if an equation has real solutions?
In the quadratic formula, if the discriminant is greater than or equal to 0, then the solutions to the quadratic equation will be real numbers. If the discriminant is less than 0, the equation has no real solution.