Page 70 - Algebra

4.1. Solving Inequalities
REMEMBER:
• When you add or subtract the same number on each side of the inequality, the inequality remains the same.
If p > q, then p + r > q + r
If p < q, then p – r < q – r
• When multiplying or dividing the same positive number on each side of the inequality, inequality remains the same.
If p > q, then p × r > q × r, r > 0
If p < q, then p ÷ r < q ÷ r, r >0
• When multiplying or dividing the same negative number on each side of the inequality, the direction of the inequality changes.
If p > q, then p × r < q × r, r < 0
If p < q, then p ÷ r > q ÷ r, r < 0
Worked Example
Find the value of x
16 – x < 11
Solution:
16 – x < 11
Subtract 11 from both sides
16 – x – 11 < 11 – 11
4– x < 0
– x< – 4
Now, multiply both sides by –1
x> 4
Page 69 of 177
Algebra I & II