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Soulver 3 0 4 X 25
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- So, 2 2 would be typed 2^2. X 2 would be typed x^2. (x+5) 2 would be typed (x+5)^2. You can put a fraction in an exponent. X 2/3 should be typed like x^(2/3). With more complicated fractions you have to use parenthesis. For example if you typed x^2+1/x-5, you might think this means 'the quantity 'x-squared plus 1' over the quantity 'x minus 5.
Graphing Linear Inequalities
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Ordered Pair | Makes the inequality 3 x + 2y≤ 6 a true statement | Makes the inequality 3 x + 2y≤ 6 a false statement |
(−5, 5) | 3(−5) + 2(5) ≤ 6 −15 +10 ≤ 6 −5 ≤ 6 | |
(−2, −2) | 3(−2) + 2(–2) ≤ 6 −6 + (−4) ≤ 6 –10 ≤ 6 | |
(2, 3) | 3(2) + 2(3) ≤ 6 6 + 6 ≤ 6 12 ≤ 6 | |
(2, 0) | 3(2) + 2(0) ≤ 6 6 + 0 ≤ 6 6 ≤ 6 | |
(4, −1) | 3(4) + 2(−1) ≤ 6 12 + (−2) ≤ 6 10 ≤ 6 |
Soulver 3 0 4 X 2
Example | ||
Problem | Use the graph to determine which ordered pairs plotted below are solutions of the inequality x – y < 3. | |
Solutions will be located in the shaded region. Since this is a “less than” problem, ordered pairs on the boundary line are not included in the solution set. | ||
(−1, 1) (−2, −2) | These values are located in the shaded region, so are solutions. (When substituted into the inequality x – y < 3, they produce true statements.) | |
(1, −2) (3, −2) (4, 0) | These values are not located in the shaded region, so are not solutions. (When substituted into the inequality x – y < 3, they produce false statements.) | |
Answer | (−1, 1), (−2, −2) |
Example | ||
Problem | Is (2, −3) a solution of the inequality | |
Unetcams multicam monitor 2 1 0 download free. y < −3x + 1 | If (2, −3) is a solution, then it will yield a true statement when substituted into the inequality y < −3x + 1. | |
−3 < −3(2) + 1 | Substitute x = 2 and y = −3 into inequality. | |
−3 < −6 + 1 | Evaluate. | |
−3 < −5 | This statement is not true, so the ordered pair (2, −3) is not a solution. | |
Answer | (2, −3) is not a solution. |
Which ordered pair is a solution of the inequality 2y - 5x < 2? A) (−5, 1) B) (−3, 3) C) (1, 5) D) (3, 3) |
Graphing Inequalities To graph an inequality: oGraph the related boundary line. Replace the <, >, ≤ or ≥ sign in the inequality with = to find the equation of the boundary line. oIdentify at least one ordered pair on either side of the boundary line and substitute those (x, y) values into the inequality. Shade the region that contains the ordered pairs that make the inequality a true statement. oIf points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for ≤ or ≥ inequalities. oIf points on the boundary line aren’t solutions, then use a dotted line for the boundary line. This will happen for < or > inequalities. |
−1 + 4(3) ≤ 4 |
−1 + 12 ≤ 4 |
11 ≤ 4 |
2 + 4(0) ≤ 4 |
2 + 0 ≤ 4 |
2 ≤ 4 |
Soulver 3 0 4 X 200
Example | |||||||
Problem | Graph the inequality 2y > 4x – 6. | ||||||
Solve for y. | |||||||
| Create a table of values to find two points on the line, or graph it based on the slope-intercept method, the b value of the y-intercept is -3 and the slope is 2. Plot the points, and graph the line. The line is dotted because the sign in the inequality is >, not ≥ and therefore points on the line are not solutions to the inequality. | ||||||
2y > 4x – 6 Test 1: (−3, 1) 2(1) > 4(−3) – 6 2 > –12 – 6 2 > −18 True! Test 2: (4, 1) 2(1) > 4(4) – 6 Browser test microphone. 2 > 16 – 6 2 > 10 False! | Find an ordered pair on either side of the boundary line. Insert the x- and y-values into the inequality 2y > 4x – 6 and see which ordered pair results in a true statement. Since (−3, 1) results in a true statement, the region that includes (−3, 1) should be shaded. | ||||||
Answer | The graph of the inequality 2y > 4x – 6 is: |
Soulver 3
When plotted on a coordinate plane, what does the graph of y ≥ x look like? A) B) C) D) |