A pan balance shows [tex]x + 2 = 10[/tex]. If you add 5 units to one side, can you balance the scale by adding [tex]x[/tex] units to the other side? Explain.

no 10-2 =8 x=8 8+8 = 16 +2 = 18 if you add 5 units to the other side it would equal 15 18 and 15 are different numbers so no

Answered by zacsanders | 2024-06-10

The question is asking whether a pan balance that initially has 'x + 2 = 10' can be kept balanced if 5 units are added to the side with 10 units and 'x' is added to the other side. To maintain balance on a double-pan mechanical balance, the weight (or mass) on both sides must be equal. In this scenario, the original equation represents a balanced scale.
To determine if the balance can be maintained after the additional weights are added, you would set up a new equation. If 5 units are added to the side where we have 10 units, that side would then have 10 + 5, which equals 15 units. Now, you want to add 'x' units to the side that initially had 'x + 2'. So, the balance equation would now be x + 2 + x = 15.
Combining like terms, the new equation is 2x + 2 = 15. Solve for x by subtracting 2 from both sides, which gives 2x = 13, and then dividing both sides by 2 which gives x = 6.5. Hence, the balance cannot be maintained by adding 'x' units to the other side since x had an original value of 8 (from x + 2 = 10) and not 6.5.

Answered by qwcat | 2024-06-24

You cannot balance the pan balance by adding x (which equals 8) to the other side after adding 5 units to one side. If you add 5 to the left, it becomes 15, while adding x to the right makes it 18. Therefore, the two sides do not equal each other, resulting in an unbalanced scale.
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Answered by zacsanders | 2024-10-24