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**Unformatted text preview: **from both sides. −2 x > −6
−2
−2 o Divide both sides by −2; reverse the symbol !
o Subtract 7 from both sides.
o Its graph is on a number line. Answer: solution set = { x | x > 3, x ∈ R } x >3
3 x Unit 3: Day 5 notes - Linear Inequalities in Two Variables exercise: Solve 5 − 3x ≥ 23 and graph its solution set. Page 2 of 4 [Answer: {x| x ≤ −6, x ∈R}]
−6 exercise: Solve 3x − 20 > −2x and graph its solution set. x [Answer: {x| x > 4, x ∈ ℝ }]
4 x LINEAR INEQUALITIES IN TWO VARIABLES
The points that make up the graph of an equation in two variables have coordinates that
satisfy the equation, ∴ all the points not on the line do not satisfy the equation.
When the coordinates of the points not on the line are substituted into the equation,
the left side will not equal the right side, so
y • EITHER the left side will be greater than the right side OR
the left side will be less than the right side.
• all the points that make the left side of the equation
greater than the right side are on one side of the line; y=x+2
2
−2 all the points that make the left side less than the right
side are on the other side of the line.
• the line from the equation forms a boundary separating the "greater than" points
from the "less than" points. To graph the solution of a linear inequality in 2 variables:
• Draw the boundary line.
o Draw the line of the equation that corresponds to the inequality.
o Use a solid line if points on the boundary satisfy the inequality;
use a dashed/broken line if points on the boundary do not satisfy the inequality.
• Determine the region with the points that satisfy the inequality.
o Choose a point on one side of the boundary and check if its coordinates satisfies
the inequality.
o If the coordinates satisfy the inequality shade that region, otherwise shade the
other region. x Unit 3: Day 5 notes - Linear Inequalities in Two Variables Page 3 of 4 example: Draw the graph of y > x + 2 . y 2 • Draw the boundary line.
−2 o The line of y = x + 2 has slope 1 and
y-intercept 2. x o Ordered pairs that satisfy the equation will not
satisfy the strictly greater than inequality. • Determine the region with solutions.
o Choose a point, (−2,2). (2) > (−2) + 2 is true;
(−2,2) does satisfy the inequality. This point is
part of the solution. y (−2,2) o Shade the region above the boundary. 2 −2 x o Points such as (0,0) on the other side of the
boundary will not satisfy the inequality. Another way to determine which side to shade:
• The inequality must be solved for y. y >x + 2 • The inequality's boundary line is y =x + 2 • For any particular value of x, say 0, the
y-coordinate of the point on the boundary
can be calculated from the equation. y y = (0) + 2 = 0 (0,2)
x • The y-coordinate of any point directly above (0,2) would have the same x-coordinate,
but a larger y-coordinate.
• These points must have coordinates that satisfy the...

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