CONCEPTUAL
For the inequality:
y<2x+1
Should the boundary line be dashed or solid?
Dashed
Solve:
x+4>9
x>5
For:
y≥3x−1
Should you shade above or below the line?
Above
A student says:
Open circles are used for:
x≤4
What is the mistake?
It should be a CLOSED circle because it is less than OR EQUAL TO.
When solving inequalities, when do you flip the inequality sign?
When multiplying or dividing by a negative number
Solve:
8v+6<62
v<7
For:
y<5x-3
Should the line be dashed or solid?
Dashed
A student solves:−2x>8 as
x>−4
What mistake did they make?
They forgot to flip the inequality sign.
Correct answer:
x<−4
True or False:
The point (0,0) is true for the following inequality:
y>x+3y
False
Solve:
9−4x≥53
x≤−11
Is the point (0,0) true or false for the following:
y<3x+1
True
A student says ∣x∣<5 means
x < 5 OR x > -5
When it is less than, we write it as two inequalities combined:
−5<x<5
What does the overlapping shaded region represent in a system of inequalities?
The solutions that satisfy BOTH inequalities
Solve:
∣n+5∣≥11
n≥6 or n≤−16
Graph:
x≤−2
Closed circle at -2, shade left
A student graphed: y≤x−2 with:
Identify BOTH mistakes.
Compare:
∣x∣<5 and ∣x∣>5
What is the BIG difference in their solutions?
∣x∣<5 means values BETWEEN -5 and 5
∣x∣>5 means values OUTSIDE -5 and 5
Solve and graph:
∣r−10∣+9>28
r>29 or r<−9
Graph:
y>x+3
Dashed line
Slope 1
Y-intercept 3
Shade above
A student says |x|>5 means
-5>x>5
When an inequality is greater than, remember greatOR than which means we must separate the inequality into two separate inequalities:
x>5 OR x < -5