Here are the list of Properties of Inequalities:
1. Additive property of inequality:
Adding the same value to both sides of the inequality does not change the inequality.
- If p < q, then p + r < q + r
- If p > q, then p + r > q + r
- If p ( leq ) q, then p + r ( leq ) q + r
- If p ( geq ) q, then p + r ( geq ) q + r
For example,
You are viewing: Which Of The Following Is Not A Property Of Inequalities
Numerical form:
5 < 9
5 + 2 < 9 + 2 (Adding 2 on both sides)
7 < 11
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Algebraic form:
(y-3 > 2)
(y-3 + 3 > 2 + 3) (Adding 3 on both sides)
(y>5)
2. Subtraction property of inequality:
Subtracting the same value from both sides of the inequality does not change the inequality.
- If p < q, then p – r < q – r
- If p > q, then p – r > q – r
- If p ( leq ) q, then p – r ( leq ) q – r
- If p ( geq ) q, then p – r ( geq ) q – r
For example,
You are viewing: Which Of The Following Is Not A Property Of Inequalities
Numerical form:
3 < 6
3 – 2 < 6 – 2 (subtracting 2 on both sides)
1 < 4
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Algebraic form:
(x+5>11)
(x+5-5>11-5) (subtracting 5 on both sides)
(x>6)
3. Multiplication property of inequality:
Let’s take two positive numbers p and q. The inequality remains the same when both p and q are multiplied by the same positive number. When both p and q are multiplied by the same negative number, however, the inequality reverses.
- If p < q and if r is a positive number, then p ( times ) r < q ( times ) r.
- If p < q and if r is a negative number, then p( times ) r > q ( times ) r
For example,
You are viewing: Which Of The Following Is Not A Property Of Inequalities
Numerical form:
7 < 9
7(times)2 < 9(times) 2 (multiplying 2 on both sides)
14 < 18
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Algebraic form:
( frac{x}{5}> 4 )
( frac{x}{5}times 5 > 4times 5 ) (multiplying 5 on both sides)
(x>20)
4. Division property of inequality:
Let’s take two positive numbers p and q. The inequality remains the same when both p and q are divided by the same positive number. When both p and q are divided by the same negative number, however, the inequality reverses.
- If p < q and if r is a positive number, then ( frac{p}{r}< frac{q}{r} )
- If p < q and if r is a negative number, then ( frac{p}{r}> frac{q}{r} )
For example,
You are viewing: Which Of The Following Is Not A Property Of Inequalities
Numerical form:
6 < 8
6 ( div ) 2 < 8 ( div ) 2 (dividing 2 on both sides)
3 < 4
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Algebraic form:
(2x>4)
( frac{2x}{2}> frac{4}{2} ) (dividing by 2 on both sides)
(x>2)
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