Graph Linear Inequalities 1
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Question 1 of 8
1. Question
Graph `x > 3`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x=3`Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)``x` `>` `3` `0` `>` `3` Plug in `0` as `x` The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `x > 3` 
Question 2 of 8
2. Question
Graph `y ≤ 2`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `y=2`Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)`.`y` `≤` `2` `0` `≤` `2` Plug in `0` as `y` The inequality is true, so we will shade the side of the line which includes the origin.Now we can graph the inequality`≤ ` means we must use a solid line when graphing `y ≤ 2` 
Question 3 of 8
3. Question
Graph `x > 4`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x=4`Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0``,0)`.`x` `>` `4` `0` `>` `4` Plug in `0` as `x` The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `x > 4` 
Question 4 of 8
4. Question
Graph `y > 2x3`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `y=``2``x``3`Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `>` `2``x``3` `0` `>` `2``(0)``3` Plug in `0` as `x` and `y` `0` `>` `3` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `y > 2x3` 
Question 5 of 8
5. Question
Graph `y ≤ 3x+2`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `y=``3``x+``2`Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `≤` `3``x``+2` `0` `≤` `3``(0)``+2` Plug in `0` as `x` and `y` `0` `≤` `2` Simplify The inequality is true, so we will shade the side of the line which includes the origin.Now we can graph the inequality`≤ ` means we must use a solid line when graphing `y ≤ 3x+2` 
Question 6 of 8
6. Question
Graph `2x+3y > 6`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `2x+3y=6`Write the equation in pointgradient form.`2x+3y` `=` `6` `2x+3y``2x` `=` `6``2x` Subtract `2x` from both sides `3y` `=` `2x+6` Simplify `y` `=` `2/3x+2` Divide both sides by `3` You may now graph the line `2x+3y=6` with its gradientintercept form.The slope of the line is `2/3` and the yintercept is `2`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`2``x``+3``y` `>` `6` `2``(0)``+3``(0)` `>` `6` Plug in `0` as `x` and `y` `0` `>` `6` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the inequality.`>` means we must use a dashed line when graphing `2x+3y > 6` 
Question 7 of 8
7. Question
Graph `x+3y3``<``0` and `xy+2 ≤ 0`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `x+3y3=0`Write the equation in pointgradient form.`x+3y3` `=` `0` `x+3y3``x+3` `=` `0``x+3` Add `x+3` to both sides `3y` `=` `x+3` Simplify `y` `=` `1/3x+1` Divide both sides by `3` You may now graph the line `x+3y3``<``0` with its gradientintercept form.The slope of the line is `1/3` and the yintercept is `1`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`x``+3``y``3` `<` `0` `0``+3``(0)``3` `<` `0` Plug `0` as `x` and `y` `3` `<` `0` Simplify The inequality is true, so we will shade the side of the line which includes the origin.Graph the line `xy+2=0`Write the equation in pointgradient form.`xy+2` `=` `0` `xy+2``x2` `=` `0``x2` Add `x2` from both sides `y` `=` `x2` Simplify `y` `=` `x+2` Divide both sides by `1` You may now graph the line `xy+2 ≤ 0` with its gradientintercept form.The slope of the line is `1` and the yintercept is `2`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`x````y``+2` `≤` `0` `0````0``+2` `≤` `0` Plug in `0` as `x` and `y` `2` `≤` `0` Simplify The inequality is not true, so we will shade the side of the line which does not include the origin.Now we can graph the two inequalities.`<` means we must use a dashed line when graphing `x+3y3``<``0``≤` means we must use a solid line when graphing `xy+2 ≤ 0` 
Question 8 of 8
8. Question
Shade the region bounded by inequalities `y≥1/2x`, `y≤2` and `y``<``2x+4`Hint
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Remember the following notations when graphing inequalities.Symbol Solid / Dotted `<` Dotted Line `>` Dotted Line `≤` Solid Line `≥` Solid Line First, treat the inequality sign as an equals sign and plot the curve.Graph the line `y=1/2x`The slope of the line is `1/2` and the yintercept is `0`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `≥` `1/2``x` `0` `≥` `1/2``(0)` Plug `0` as `x` and `y` `0` `≥` `0` Simplify The inequality is true, so we will shade the side of the line which includes the origin.`≥` means we must use a solid line when graphing `y≥1/2x`Graph the line `y=2`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(0,``0``)`.`y` `≤` `2` `0` `≤` `2` Plug `0` as `y` The inequality is true, so we will shade the side of the line which includes the origin.`≤` means we must use a solid line when graphing `y≤2`Graph the line `y=2x+4`The slope of the line is `2` and the yintercept is `4`.Use a test point to see which side of the line is to be shaded. We can try the origin, `(``0,0``)`.`y` `<` `2``x``+4` `0` `<` `2``(0)``+4` Plug `0` as `x` and `y` `0` `<` `4` Simplify The inequality is true, so we will shade the side of the line which includes the origin.`<` means we must use a dashed line when graphing `y``<``2x+4`Now we can graph the three inequalities.
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