(3x-3) > 9
Multiply both sides by 5 to clear the fraction.
(The > symbol does not reverse when we multiply
or divide both sides by a positive number)
(5)·(3x-3) > (5)·9
3(3x-3) > 45
9x - 9 > 45
9x > 54
Divide both sides by 9.
(The > symbol does not reverse when we multiply
or divide both sides by a positive number)
>
x > 6
To write the solution set in set-builder notation:
{x | x > 6}
-----------------------------------------------------
0.4x + 6 ≤ 1.2x - 3
Clear of decimals by multiplying through every term by 10
(10)·0.4x + (10)·6 ≤ (10)·1.2x - (10)·3
4x + 60 ≤ 12x - 30
4x ≤ 12x - 90
-8x ≤ -90
We divide both sides by -8. But when we multiply or
divide both sides of an inequality by a negative number,
the inequality symbol is reversed:
≥
x ≥
x ≥ 11.25
To write the solution set in set-builder notation:
{x | x ≥ 11.25}
------------------------------------------------------
x ≥
Clear both fractions by multiplying both sides by -16.
But when we multiply or divide both sides of an inequality
by a negative number, the inequality symbol is reversed:
(-16)·x ≥ (-16)·
14x ≤ 3
Divide both sides by 14.
(The > symbol does not reverse when we multiply
or divide both sides by a positive number)
≤
x ≤
To write the solution set in set-builder notation:
{x | x ≤ }
Edwin
