Solving Compound Inequalities Equations
Key Concepts
- Define a compound inequality
- Solve a compound inequality involving “or”
- Solve a compound inequality involving “and”
- Use compound inequality to solve problems
Compound Inequality
- A compound inequality is made of two or more inequalities.
Step 1: Write an inequality to represent the solutions shown in each part of the graph.
Step 2: Draw the compound inequality.
The compound inequality describes the graph of x ≤ -3 or x > 2.
Solve compound inequality including “or”
- When a compound inequality with an “or” is given, the graph shows all points that appear in either of the solutions above.
Example: Solve 2x-5 > 3 or -4x+7 < -25
Step 1: Solve and graph 2x-5 > 3
2x-5+5 > 3+5
2x > 8
2x/2 > 8/2
x > 4
Step 2: Solve and graph 4x-7 < 25
4x+7–7 < 25+7
4x < 32
4x/4 < 32/4
x < 8
The solutions can be 5, 6, 7.
Solving compound inequality including “and”
- When a compound inequality with an “and” is given, the final graph shows all points that appear in both solutions above.
Example: Solve -12 ≤ 7x+9 < 16
Step 1: Solve and graph -12 ≤ 7x+9
-12 – 9 ≤ 7x + 9 – 9
-21 ≤ 7x
−217 ≤ 7x/7
-3 ≤ x
Step 2: Solve and graph 7x+9 < 16
7x+9-9 < 16-9
7x < 7
7x/7 < 7/7
x < 1
The solution is x ≥ -3 and x<1, or -3≤x<1
Exercise
- Solve 12<2x<28
- The compound function that represents the graph is _________.
- Write the compound inequality that represents the area A of the rectangle if 35≥A≥25
- Find the area of the right-angled triangle if the height is 5 units and the base is x units, given that the area of the triangle lies between 10 and 35 sq. units.
- Write an inequality that represents the quantity that is greater than 18 but less than or equal to 27
Concept Map
What have we learned
- A compound equality is made up of two or more inequalities.
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