Solve and Graph Inequalities
Solve and Graph Inequalities
Objectives:
-Solve and graph linear inequalities.
Common Core Standards:
A.CED.1 - Create equations and inequalities in one variable and use them to solve
problems.
A.REI.3 - Solve linear equations and inequalities in one variable, including
equations with coefficients represented by letters.
A.CED.3 - Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or nonviable options
in a modeling context.
© Ashley Spencer, 2013
Solve and Graph Inequalities
Inequalities
>
"is greater than"
<
"is less than"
≥
"is greater than or equal to"
≤
"is less than or equal to"
Solving Inequalities: Algebraic answer AND Graph answer
Answer must be in x > number form (the variable always goes on the left.)
© Ashley Spencer, 2013
Solve and Graph Inequalities
How to graph inequalities: Arrow goes toward where the true solutions are.
"The answer is greater than or equal to five"
-Solid Dot
-Arrow to the right
<---Why is this not a good representation?
"The answer is greater than five"
-Open Dot
-Arrow to the right
© Ashley Spencer, 2013
Solve and Graph Inequalities
Solve and graph the following inequalities.
m-9<2
4x > 12
"The answer is greater than three"
"The answer is less than eleven"
-Open Dot
-Open Dot
-Arrow to the Right
-Arrow to the Left
© Ashley Spencer, 2013
Solve and Graph Inequalities
Solve and graph the following inequalities.
3≥c+5
3+x>4
Remember the variable must go first or the expression doesn't make sense!
Answer: c ≤ -2
© Ashley Spencer, 2013
Solve and Graph Inequalities
If you multiply or divide by a negative, you must flip the inequality sign!!!
Solve and graph the following inequality.
-8k ≥ 16
Flip the inequality symbol!
© Ashley Spencer, 2013
Solve and Graph Inequalities
Solve and graph the following inequalities.
x
2
> -5
2y - 3 < -3
© Ashley Spencer, 2013
Solve and Graph Inequalities
Solve and graph the following inequalities.
-1 < 9 +
2
3
g
-
Remember the variable must go first!
Answer: g > -15
© Ashley Spencer, 2013
r
3
≤ -5
Solve and Graph Inequalities
Variables on Both Sides: Could yield All Solutions (True) or No Solution (False)
Solve and graph the following inequalities.
x+4>x+2
2b - 1 < -2 + 2b
© Ashley Spencer, 2013
Solve and Graph Inequalities
Solve and graph the following inequalities.
6x - 3 < 7 + 4x
2(x - 4) ≤ 6
© Ashley Spencer, 2013
Solve and Graph Inequalities
Error Analysis
Julie and Jamie are solving 6d ≥ -84. Is either of them correct? Explain your reasoning.
Julie
Jamie
6d#≥#%84
6d#≥#%84
6d#≥#%84
6d#≥#%84
##6#######6
##6#######6
d#≥#%14
d#≤#%14
© Ashley Spencer, 2013