Graph the inequality and find the solution sets;
1. { x>2 { y>>
2.{ 2x+3y≥4 { 2x-y
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Graph the inequality and find the solution sets;
1. { x>2 { y>>
2.{ 2x+3y≥4 { 2x-y
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Answer:
I can help explain how to graph the inequalities and find the solution sets. ikaw na mag graph (intindihin mo lang)
1. Graphing the inequality x > 2:
To graph this inequality, we need to draw a dashed vertical line at x = 2 (since x is greater than 2, not including 2 itself). Then, shade the region to the right of the line to represent all the values of x that are greater than 2.
Solution set: {x | x > 2}
2. Graphing the inequality 2x + 3y ≥ 4:
To graph this inequality, we can start by graphing the equation 2x + 3y = 4, which represents the boundary line. To do this, we can rewrite the equation in slope-intercept form: y = (-2/3)x + 4/3. Plot the y-intercept at (0, 4/3), and use the slope (-2/3) to find additional points on the line. Draw a solid line to represent the boundary.
Next, we need to determine which side of the line to shade. Since the inequality is greater than or equal to (≥), we shade the region that includes the line. In this case, it is the region above the line.
Solution set: {(x, y) | 2x + 3y ≥ 4}
3. Graphing the inequality 2x - y < 0:
To graph this inequality, we can start by graphing the equation 2x - y = 0, which represents the boundary line. To do this, we can rewrite the equation in slope-intercept form: y = 2x. Plot the y-intercept at (0, 0), and use the slope (2) to find additional points on the line. Draw a dashed line to represent the boundary.
Next, we need to determine which side of the line to shade. Since the inequality is less than (<), we shade the region that does not include the line. In this case, it is the region below the line.
Solution set: {(x, y) | 2x - y < 0}
Please note that without a visual graph, it is important to interpret the solution sets based on the explanations provided.