Question

Plz help!!! You identify the error the solve it correctly!!!!!

Answer 1

Answer:

You have to multiply the numbers diagonally not vertically.

So

10x = 7(350)

10x = 2450

x = 245

Answer 2

9514 1404 393

Answer:

• different sides of the equation were multiplied by different numbers
• x = 245

Step-by-step explanation:

There is a method of solving proportions that is called "cross multiply" or "cross multiplication". For a proportion like this it looks like each numerator is multiplied by the opposite denominator. In this problem, the result would be ...

  7(350) = (10)x

While "cross multiplication" is a description of the appearance of what is happening, what is really happening is that both sides of the equation are being multiplied by the same value: the product of the denominators. This is in accordance with the multiplication property of equality, which requires you multiply both sides of the equation by the same value.

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The error that was made in this problem is that each numerator was multiplied by its own denominator. Effectively, that multiplied the left side of the equation by 10² = 100, and the right side of the equation by 350² = 122500. This is in direct violation of the multiplication property of equality, so guarantees the value found for x will be wrong.

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While "cross multiply" is an instruction often given for solving proportions, it causes an extra step to be needed in solving a proportion like this one. All that is really needed is to multiply both sides of the equation by the denominator under the variable. Here, that means multiplying both sides of the equation by 350.

Correct solution

  $\dfrac{7}{10}=\dfrac{x}{350}\\\\350\cdot\dfrac{7}{10}=350\cdot\dfrac{x}{350}\\\\\\35\cdot 7=\boxed{x=245}$