Page 78 - Algebra

4.3. Properties of Inequalities
REMEMBER:
• If n > 0 and p > q > 0 pm > qm
p-m < q-m
11 𝑝𝑚 >𝑞𝑚
• If n > 0 and p < q, p > 0, q > 0 pm < qm
p-m > q-m
11 𝑝𝑚 <𝑞𝑚
• If p > 0, then p + 1 ≥ 2 𝑝
• If p < 0, then p + 1 ≤ –2 𝑝
4.4. Graphing Inequalities in Two Variables
A horizontal or a vertical line will divide the Cartesian plane into two halves or half-planes.
• A vertical line divides left and right half-plane
• A horizontal line divides in an upper and lower half-plane
To graph an inequality in two variables such as px + qy > r, first plot px + qy = r. Let's understand it using an example.
Graph y > x – 5
Draw the graph of y = x – 5 or y – x = – 5
The equation will divide the plane into two planes, as shown.
When the inequality does not have an equal to sign (< or >), use a dashed or a dotted line because the solution can never lie on the line.
Page 77 of 177
Algebra I & II