What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 3

What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 3

The region is a square with vertices (3,0), (0,3), (3,0), (0, - 3)
Its area is 1 / 2 * 3 * 3 * 4 = 18

What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 2

2*2/2*4=8
The area is 8

Draw the plane area represented by the inequality | x | + | y ≤ 1

chart

Draw the plane area represented by the following inequality 2x-y＞2 y≤-2 x≥3 There is also a plane region of inequality rent -x+y-2≤0 x+y-4≤0 x-3y+3≤0

method:
Draw a straight line first
2x-y=2
y=-2
X=3
Then Y > is above the line and Y < is below the line
If it's - Y >, it's the bottom that translates to y < 0
Below the 2x-y > 2 line
Under y ≤ - 2 line
X ≥ 3, this is a vertical line. You should know
The method of the second question is the same
I hope to give you fish

Solving the inequality [image method] - x 2 ＋ 2x-1 ≥ 0 2x ＋ X -- 1 ≤ 0 -- X? - 2x ≥ - 3

Why to use the image method to solve the quadratic inequality of one variable? If we use the image method, we still need to consider the opening direction, the symmetry axis, and the intersection of the coordinate axis, which is much more troublesome than the direct solution!
(1) -X²＋2X－1≥0
X²-2X+1≤0
That is (x-1) 2 ≤ 0
Because (x-1) 2 ≥ 0 is constant
So only (x-1) 2 = 0, that is, x = 1
(2) 2X²＋X--1≤0
(2x-1)(x+1)≤0
So - 1 ≤ x ≤ 1 / 2
(3) --X²－2X≥﹣3
X²+2x-3≤0
(x+3)(x-1)≤0
-3≤x≤1

Solving inequality by image method: 3 / 2x-2

Let Y1 = 3 / 2x-2, y2 = - x + 3
Y1, Y2
Y1 in image

Using the image method to solve the quadratic inequality of one variable: the square of x-2x-3 > 0, and let y = the square of x-2x-3, then y is the quadratic function of X, because a = 1 > 0, so we can discard the quadratic function of X So the opening of the parabola is upward, and because when y = 0, the square of X - 2x-3 = 0, the solution X1 = - 1, X2 = 3, because the approximate image of the parabola y = x square - 2x-3, when X3, Y > 0, so the solution set of square - 2x-3 > 0 of X is: x3,1, directly write the square - 2x-30 of the quadratic inequality X

1, write directly the square - 2x - 3 of the quadratic inequality X of one variable

In this paper, we use the image method to solve the univariate quadratic inequality: x? - 2x-3 > 0, and let y = x? - 2x-3, then y is the quadratic function of X, because a = 1 > 0, so we can discard the equation The opening of the object line is upward, and when y = 0, the square of x-2x-3 = 0, the solution of X1 = - 1, X2 = 3, because the approximate image of the parabola y = x square-2x-3, when X3, Y > 0, so the solution set of X square-2x-3 > 0 is: X3 1. According to the above example, the image method is used to solve the univariate quadratic inequality x? Ax-2a? 0, 2. According to the above example, the image method is used to solve the univariate quadratic inequality AX2 - (A-2) x + 2 > 0

Factorization, (x-2a) (x + a) > 0, the coefficient of quadratic term is positive, so take between two, when a < 0, 2ao, - A (AX-2) (x-1) > 0 A2 / A, a > √ 2, x < 2 / A, x > 1, pure hand typing, score

Solving inequality system 2-5x > 1 / 2x, 5x-4 > 6x-1 To solve the system of univariate linear inequalities: (1) 2-5x > 1 / 2x, 5x-4 > 6x-1 (2)7x+8

（1）x

5x-1 > 2x + 55x-3 = x + 2 use function image to solve inequality! How to solve it? For example: is it possible to solve the problem of 3x-6 > 0 in the end? Is it 3x-6 > y? According to this to draw the image? The book says: 3x-6 can = y? What's going on? How to write the first one? How to write it into the form of y = KX + B? It is to write the form of 5x-3 = x + 2 → 4x-5 = 0 → 4x-5 = y? And then go out to solve the problem?! Please help me! Please It's better to have an explanation!

Draw the images of 2x-5 and 2x-1 respectively
Find their intersection point, that is, the solution x = 2, y = 9
You can see that the answer is x > 2
In the same way, think about it yourself