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Graph the following inequalities:
a. y > -3
b. x ≤ 2
c. 3x + 4y + 12 > 0
d. 2x - y ≤ 8
Solution:
a. For y > -3, the given line is a horizontal line. Since the sign of inequality is greater than, then all points along the line are not included in the solution. However, all points above the given line are included in the solution. Here's the graph of the given line
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| Photo by Math Principles in Everyday Life |
b. For x ≤ 2, the given line is a vertical line. Since the sign of inequality is less than or equal to, then all points along the line are included in the solution. However, all points at the left of the given line are included in the solution. Here's the graph of the given line
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| Photo by Math Principles in Everyday Life |
c. For 3x + 4y + 12 > 0, we need to rewrite the given equation into slope-intercept form as follows
Since the sign of inequality is greater than, then all points along the line are not included in the solution. If x = 0 and y = 0, then the given equation reduces to 12 > 0 which is correct and that point is included in the solution. Therefore, the graph of the given equation is
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| Photo by Math Principles in Everyday Life |
d. For 2x - y ≤ 8, we need to rewrite the given equation into slope-intercept form as follows
If you divide both sides of the equation by a negative number, then the sign of inequality will be reversed. Since the sign of inequality is less than or equal to, then all points along the line are included in the solution. If x = 0 and y = 0, then the given equation reduces to 0 ≤ 8 which is correct and that point is included in the solution. Therefore, the graph of the given equation is
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| Photo by Math Principles in Everyday Life |