Franklin is drawing a rectangle. The length will be 5 inches, and the area will be at least 20
1 answer:
Given:
Length of the rectangle = 5 inches
Width of the rectangle = x
Area of the rectangle is at least 20 square inches.
To find:
The inequality for the given problem.
Solution:
Let x represent the width of the rectangle.
We know that the area of a rectangle is:
It is given that, the area of the rectangle is at least 20 square inches. It means the area of the rectangle must be greater than or equal to 20.
Therefore, the required inequity for the given problem is .
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Check the picture below.
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line <span>y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike </span>⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line <span>y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike </span>⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.