Give me an example of scale balance illustrating inequalities

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.

30

step-by-step explanation:

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