Introduction for conditional inequality:
Inequalities are algebraic equations and it variable x cannot be equal. Inequalities has the different values. In adding algebraic equation we use the different arithmetic operators like <, >, =, = that will form an inequality. When we set values for variables in an inequality equation, if it gives true only for some particular value then that inequality is known as conditional inequality.
Solution of a Conditional Inequality:
Let x is the solution of conditional inequality which consists of all values of x for which the inequality is true these values lie on one or more intervals of the real number scale .
Example problem for conditional inequality:
Ex 1: x - 6 > 0
Sol : x - 6 > 0
Add 6 on both sides,
x - 6 + 6 > 0 + 6
x > 6
Only when x value is greater than 6 the inequality satisfies the condition x - 6 > 0. Hence it is conditional inequality.
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Example Problems on Conditional Inequalities:
Ex 1: Solve the conditional inequality : x + 12 < 8
Sol : Subtract12 from each side:
x + 12 - 12 < 8 - 12
x < - 4
this means that any number less than - 4 only will make the equation "x + 12 < 8" true!
Ex 2: Solve the conditional inequality 4x+7 > 5
Sol : 4x + 7 > 5
Subtract 7 on both sides
4x + 7 - 7 > 5 - 7
4x > - 2
Divide both sides by 2
4x / 2 > - 1
x > - 1 / 2
This means that any number greater than - 1 / 2 will make the equation "4x + > 7 " true!
Ex 3 : The length of Asha’s rectangular library is 8 ft. If the area of the library is at least 104 square feet, what is the smallest width the library could have?
Sol : Here we need to find width. Let width be w. We know that,
Area = length * Width.
So Area = 8 w. Since Area is at least 104,
Area = 104
Substituting 12w into the inequality for Area we have,
8w = 104
Solve the conditional inequality by dividing both sides by 8 and we have,
w = 13
The length of the library must be at least 6 feet.
Inequalities are algebraic equations and it variable x cannot be equal. Inequalities has the different values. In adding algebraic equation we use the different arithmetic operators like <, >, =, = that will form an inequality. When we set values for variables in an inequality equation, if it gives true only for some particular value then that inequality is known as conditional inequality.
Solution of a Conditional Inequality:
Let x is the solution of conditional inequality which consists of all values of x for which the inequality is true these values lie on one or more intervals of the real number scale .
Example problem for conditional inequality:
Ex 1: x - 6 > 0
Sol : x - 6 > 0
Add 6 on both sides,
x - 6 + 6 > 0 + 6
x > 6
Only when x value is greater than 6 the inequality satisfies the condition x - 6 > 0. Hence it is conditional inequality.
Please express your views of this topic what are linear equations by commenting on blog.
Example Problems on Conditional Inequalities:
Ex 1: Solve the conditional inequality : x + 12 < 8
Sol : Subtract12 from each side:
x + 12 - 12 < 8 - 12
x < - 4
this means that any number less than - 4 only will make the equation "x + 12 < 8" true!
Ex 2: Solve the conditional inequality 4x+7 > 5
Sol : 4x + 7 > 5
Subtract 7 on both sides
4x + 7 - 7 > 5 - 7
4x > - 2
Divide both sides by 2
4x / 2 > - 1
x > - 1 / 2
This means that any number greater than - 1 / 2 will make the equation "4x + > 7 " true!
Ex 3 : The length of Asha’s rectangular library is 8 ft. If the area of the library is at least 104 square feet, what is the smallest width the library could have?
Sol : Here we need to find width. Let width be w. We know that,
Area = length * Width.
So Area = 8 w. Since Area is at least 104,
Area = 104
Substituting 12w into the inequality for Area we have,
8w = 104
Solve the conditional inequality by dividing both sides by 8 and we have,
w = 13
The length of the library must be at least 6 feet.
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