Addition and subtraction properties of inequality :
When you add or subtract the same number from each side of an inequality, the inequality remains true.
Algebra : x < y x + z < x + z |
Algebra : x < y x - z < y - z |
Addition property Numbers : 3 < 7 3 + 2 < 7 + 2 5 < 9 |
Subtraction property Numbers : 3 < 7 3 - 2 < 7 - 2 1 < 5 |
These properties are also true for >, ≤ and ≥
To see more examples
Multiplication and division properties of inequality :
When you multiply or divide each side of an inequality by the same positive number, the inequality remains true.
Algebra : If x < y and z > 0, then, x × z < y × z |
Algebra : If x < y and z > 0, then, x/z < y/z |
Multiplication property Numbers : 3 < 7 3 × 2 < 7 × 2 6 < 14 |
Division property Numbers : 25 < 40 25/5 < 40/5 5 < 8 |
These properties are also true for >, ≤ and ≥
To see more examples
Multiplication and division properties of inequality :
Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
Algebra : If x < y and z < 0, then, x × z > y × z |
Algebra : If x < y and z < 0, then, x/z > y/z |
Multiplication property Numbers : 2 < 4 2 × (-2) < 4 × (-2) -4 > -8 |
Division property Numbers : 2 < 4 2 / (-2) < 4 / (-2) -1 > -8 |
Solve the inequalities using addition and subtraction property :
Example 1 :
y - 4 > -7
Solution :
y - 4 > -7
Because 4 is subtracted from y, add 4 to each side to undo the subtraction.
(y - 4) + 4 > (-7) + 4
y - 4 + 4 > -3
y > -3
Example 2 :
0.9 ≥ a - 0.2
Solution :
0.9 ≥ a - 0.2
Because 0.2 is subtracted from a, add 0.2 to each side to undo the subtraction.
(0.9) + 0.2 ≥ (a - 0.2) + 0.2
0.9 + 0.2 ≥ a - 0.2 + 0.2
0.11 ≥ a
a ≤ 0.11
Example 3 :
x + 7 < 13
Solution :
x + 7 < 13
Because 7 is added to x, subtract 7 from each side to undo the addition.
(x + 7) - 7 < (13) - 7
x + 7 - 7 < 13 - 7
x < 6
Example 4 :
b + 6.2 ≥ 9.2
Solution :
b + 6.2 ≥ 9.2
Because 6.2 is added to b, subtract 6.2 from each side to undo the subtraction.
(b + 6.2) - 6.2 ≥ (9.2) - 6.2
b + 6.2 - 6.2 ≥ 9.2 - 6.2
b ≥ 3
Solve the inequalities using multiplication and division property :
Example 5 :
y/2 > -1.5
Solution :
y/2 > -1.5
Because y is divided by 2, multiply each side by 2 to undo division.
2(y/2) > 2(-1.5)
y > -3
Example 6 :
-b/10 ≥ -0.11
Solution :
-b/10 ≥ -0.11
Because -b is divided by 10, multiply each side by -10 and change ≥ to ≤.
(-b/10)(-10) ≤ -0.11(-10)
10b/10 ≤ 1.1
b ≤ 1.1
Example 7 :
3x < 18
Solution :
3x < 18
Because x is multiplied by 3, divide each side by 3 to undo the multiplication.
3x/3 < 18/3
x < 6
Example 8 :
-10a > 15
Solution :
-10a > 15
Because a is multiplied by -10, divide each side by -10 and change > to <.
-10a/(-10) < 15/(-10)
a < -1.5
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