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Linear Inequalities
Linear Inequalities
Standard
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane...and graph the solution...to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Recall Inequalities
Recall Inequalities
Linear Inequalities are line equations but with inequalities
Linear Inequalities are line equations but with inequalities
So instead of this
So instead of this
The equals sign is replaced with an inequality sign
The equals sign is replaced with an inequality sign
How to check for solutions to the inequality
How to check for solutions to the inequality
Is (3,6) a solution of y ≤ 2x + 4? Is (2, 10) a solution?
Is 6 less than or equal to 10? Yes, it is. So (3,6) is a solution to this linear inequality.
Is 6 less than or equal to 10? Yes, it is. So (3,6) is a solution to this linear inequality.
Is 10 less than or equal to 8? No, it is not. So (2,10) is not a solution to this linear inequality.
Is 10 less than or equal to 8? No, it is not. So (2,10) is not a solution to this linear inequality.
How to solve for y
How to solve for y
As usual, the inequality might not have y isolated on one side. Solve for y like you usually would, except with one major rule:
As usual, the inequality might not have y isolated on one side. Solve for y like you usually would, except with one major rule:
If you multiply or divide by a negative number on both sides of the equation, flip the direction of the signs!
If you multiply or divide by a negative number on both sides of the equation, flip the direction of the signs!
Example
Example
Given -2y + 4x ≥ 12, solve for y.
This is what we mean by flipping the direction of the sign. We divided by -2 to isolate the y. Since it's negative, we flipped the sign.
This is what we mean by flipping the direction of the sign. We divided by -2 to isolate the y. Since it's negative, we flipped the sign.
Keywords: linear inequality, y=mx+b, line
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