Algebraic Inequalities
Algebraic inequality statements are solved in the same manner as equations. However, do not forget that whenever you multiply or divide by a negative number, the order of the inequality, that is, the inequality symbol must be reversed. In reading the inequality symbol, remember that it points to the smaller quantity. a < b is read a is less than b. a > b is read a is greater than b.
Example:
Solve for x: 12 – 4x < 8
Solution:
Add –12 to each side.
–4x < –4
Divide by –4, remembering to reverse the inequality sign.x>1
Example:
6x + 5 > 7x + 10
Solution:
Collect all the terms containing x on the left side of the equation and all numerical terms on the right. As with equations, remember that if a term comes from one side of the inequality to the other, that term changes sign.
–x > 5
Divide (or multiply) by –1.x < –5
Algebraic inequality statements are solved in the same manner as equations. However, do not forget that whenever you multiply or divide by a negative number, the order of the inequality, that is, the inequality symbol must be reversed. In reading the inequality symbol, remember that it points to the smaller quantity. a < b is read a is less than b. a > b is read a is greater than b.
Example:
Solve for x: 12 – 4x < 8
Solution:
Add –12 to each side.
–4x < –4
Divide by –4, remembering to reverse the inequality sign.x>1
Example:
6x + 5 > 7x + 10
Solution:
Collect all the terms containing x on the left side of the equation and all numerical terms on the right. As with equations, remember that if a term comes from one side of the inequality to the other, that term changes sign.
–x > 5
Divide (or multiply) by –1.x < –5
If x < 0 and y > 0, which of the following will always be greater than 0?
(A) x+y
(B) x–y
(C)x/y
(D) xy
(E) –2x
E
The product of two negative numbers is positive.
(A) x+y
(B) x–y
(C)x/y
(D) xy
(E) –2x
E
The product of two negative numbers is positive.
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