Answer: 3x + 1 < 5 which has the same scale as x < 4/3
Step-by-step explanation:
Scale balance involves operating on each side of an equation or inequality, by adding, subtracting, multiplying, or dividing by a certain quantity, without changing the equilibrium of the equation or inequality.
The rules are easy,
* Everything you add to, subtract from, divide with, or multiply by one side of an equation or inequality must be done to the other side.
On Inequalities <, >, ≥, and ≤
* Anything you add, subtract, divide or multiply by the left hand side, the same must be done to the right hand side.
* Anytime you divide by a negative quantity, the inequality changes, and you must change the inequality sign.
Change < to > and vice versa.
Change) ≤ to ≥ and vice versa.
Example
Consider the following inequality.
3x + 1 < 5
subtract 1 from both sides of the inequality
3x + 1 - 1 < 5 - 1
3x < 4
Divide both sides of the inequality by 3
3x/3 < 4/3
x < 4/3
Here is another example.
Consider the following inequality
2y + 1 ≤ 5y + 9
Subtract 1 from both sides
2y + 1 - 1 ≤ 5y + 9 - 1
2y ≤ 5y + 8
Subtract 5y from both sides
2y - 5y ≤ 5y + 8 - 5y
-3y ≤ 8
Divide both sides by -3, but remember, DIVIDING BY A NEGATIVE QUANTITY CHANGES THE INEQUALITY .
-3y/-3 ≥ 8/(-3)
y ≥ -8/3 or -2⅔
I hope this helps, good luck.
