SOLVING COMPOUND INEQUALITIES EXAMPLES
About "Solving compound inequalities examples"
Solving compound inequalities examples :
Here we are going to see some examples based on the concept solving compound inequalities.
A compound inequality is an equation with two or more inequalities joined together with either "and" or "or" (for example, x ≥ 6 and x < 3; x < -12 or x ≥ 8).
Compound inequalities with "And" :
A compound inequality containing and is true only if both inequalities are true. Thus, the graph of a compound inequality containing and is the intersection of the graphs of the two inequalities.
In other words, the solution must be a solution of both inequalities.
The intersection can be found by graphing each inequality and then determining where the graphs overlap.
Compound inequalities with "Or" :
Another type of compound inequality contains the word or. A compound inequality containing or is true if one or more of the inequalities is true. The graph of a compound inequality containing or is the of the graphs of the two inequalities.
In other words, the solution of the compound inequality is a solution of either inequality, not necessarily both. The union can be found by graphing each inequality.
Example 1 :
Solve the compound inequality. Then graph the solution set
k + 2 > 12 and k + 2 ≤ 18
Solution :
|
k + 2 > 12 Subtract by 2 on both sides k + 2 - 2 > 12 - 2 k > 10 |
k + 2 ≤ 18 Subtract by 2 on both sides k + 2 - 2 ≤ 18 - 2 k ≤ 16 |
By graphing the inequality k > 10, we get the graph given below.
By graphing the inequality ≤ 16, we get the graph given below.
By combining the above two graphs, we get the common region between 10 and 16.
Example 2 :
Solve the following inequality and graph the solution
3 < 2x - 3 < 15
Solution :
3 < 2x - 3 < 15
Add 3 on both sides
3 + 3 < 2x – 3 + 3 < 15 + 3
6 < 2x < 18
Divide by 2
6/2 < 2x/2 < 18/2
3 < x < 9
Example 3 :
Solve the following inequality and graph the solution
3t – 7 ≥ 5 and 2t + 6 ≤ 12
Solution :
3t – 7 ≥ 5 and 2t + 6 ≤ 12
|
3t – 7 ≥ 5 Add 7 on both sides 3t – 7 + 7 ≥ 5 + 7 3t ≥ 12 Divide by 3 on both sides 3t/3 ≥ 12/3 t ≥ 4 |
2t + 6 ≤ 12 Subtract 6 on both sides 2t + 6 – 6 ≤ 12 – 6 2t ≤ 6 Divide by 2 on both sides t ≤ 3 |
t ≥ 4 and t ≤ 3
Example 4 :
Solve the following inequality and graph the solution
4m - 5 > 7 or 4m - 5 < -9
Solution :
|
4m - 5 > 7 Add 5 on both sides 4m - 5 + 5 > 7 + 5 4m > 12 Divide by 4 on both sides 4m/4 > 12/4 m > 3 |
4m - 5 < -9 Add 5 on both sides 4m - 5 + 5 < -9 + 5 4m < -4 Divide by 4 on both sides 4m/4 < -4/4 m < -1 |
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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
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Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
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Word problems on simple interest
Word problems on compound interest
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Complementary and supplementary angles word problems
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Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
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Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
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Domain and range of rational functions with holes
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L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
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