Draw the line x = -1 which is a vertical line (parallel to the y-axis) that goes through (-1 , 0)
Shade the side to the left of it as those numbers are less than -1.
use a line graph. Place a solid dot at 4. Shade the entire region to the left of 4.x is Less than shade Left.* * * * * The above answer is so very wrong - it has missed out the key word "absolute".Use a line graph. Put a solid dot at -4 and another solid dot at +4 and join them. Every point on the line (including the two end points) is the graph.
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If the inequality is strict (< or >) then the boundary is not included. Otherwise (≤ or ≥), it is.
if you have y <= f(x), then graph the function y = f(x) with a solid line, then shade everything below that graph.
y >= -3 + xThis is the same asy>= x-3Start off by sketching the regular graph of y=x-3 (should look the same as the graph of y=x but shifted down 3 places so that the y intercept is at the point (0,-3)).Now just shade the half of the graph where y is greater (so shade in the positive direction for y above the graph of the line).In the end you should have the graph of a diagonal line shaded over the top.***Note: You will draw your graph with a solid line because because the question says GREATER THAN OR EQUAL TO. If you ever get a graph that is strictly greater than or strictly less than, instead of drawing a solid line, draw a dotted line, to show that you're not including the values where y is equal to your function.If you get y> shade in the positive y direction and use a dotted line.................y< shade in the negative y direction and use a dotted line.................y>= shade in the positive y direction and use a solid line.................y
If the graph is a two-dimensional plane and you are graphing an inequality, the "greater than or equal to" part will be shown by two things: (1) a solid, not a dotted, line--this part signifies the "or equal to" option--and (2) which region you shade. Shade the region that contains the points that make the inequality true. By shading that region, you are demonstrating the "greater than" part.
use a line graph. Place a solid dot at 4. Shade the entire region to the left of 4.x is Less than shade Left.* * * * * The above answer is so very wrong - it has missed out the key word "absolute".Use a line graph. Put a solid dot at -4 and another solid dot at +4 and join them. Every point on the line (including the two end points) is the graph.
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In a plane, it is the area to the left of the vertical line through x = -1. Since it is not a strict inequality, the line should be drawn solid (not dashed or dotted).
If the inequality is strict (< or >) then the boundary is not included. Otherwise (≤ or ≥), it is.
if you have y <= f(x), then graph the function y = f(x) with a solid line, then shade everything below that graph.
y >= -3 + xThis is the same asy>= x-3Start off by sketching the regular graph of y=x-3 (should look the same as the graph of y=x but shifted down 3 places so that the y intercept is at the point (0,-3)).Now just shade the half of the graph where y is greater (so shade in the positive direction for y above the graph of the line).In the end you should have the graph of a diagonal line shaded over the top.***Note: You will draw your graph with a solid line because because the question says GREATER THAN OR EQUAL TO. If you ever get a graph that is strictly greater than or strictly less than, instead of drawing a solid line, draw a dotted line, to show that you're not including the values where y is equal to your function.If you get y> shade in the positive y direction and use a dotted line.................y< shade in the negative y direction and use a dotted line.................y>= shade in the positive y direction and use a solid line.................y
The equation 0 equals 0 is an identity and contributes absolutely nothing to the part of the graph that you should shade or not. The tautological statement can be ignored.
If you mean with inequalities: 1. Change the inequality into an equation.2. Solve the equation for the initial line.3. Look back to the inequality.a.) greater than or equal to-shade above or to the left of your line,this line should be solidb.) greater than-shade above or to the left of your line,this line should not be solidc.) less than or equal to-shade below or to the right of your line,this line should be solidd.) less than-shade below or to the right of your line,this line should not be solidHope this helps.
Linear programming is just graphing a bunch of linear inequalities. Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it in the inequality, and the it the point makes the inequality true (like 0
At negative six on the x-axis, draw a vertical line. That line will be a solid line because we have that x is greater than OR EQUAL TO negative six. Then shade the right half of the graph -- which is where x has a value that is to the right (greater than) negative six
Arrange the inequality so that the variable is on the left. ex x < 7 If not equal to put an open circle at the number (7 in my example) if less than shade the number line to the left ( less than = shade left) if greater than shade right. If equal to put a point ( shaded dot) on the number follow same rules for shading