Question

Write the equation 5(x−7)=6(y−8) in standard form.

Answer 1

The equation 5(x−7)=6(y−8) in standard form is 5x - 35 = 6y - 48.

Step-by-step explanation:

To convert the given equation to standard form, we need to distribute the constants outside the parentheses and simplify the expression. Starting with 5(x−7)=6(y−8), distribute the 5 on the left side to both terms inside the parentheses:

`\[5x - 35 = 6(y - 8).\]`

Next, distribute the 6 on the right side to both terms inside its parentheses:

`\[5x - 35 = 6y - 48.\]`

Now, we have the equation in the form 5x - 35 = 6y - 48. To put it in standard form, we typically arrange the terms so that the variables are on one side and constants on the other. Let's move all terms to the left side:

`\[5x - 6y = -13.\]`

This is the standard form of the given equation. In standard form, the coefficients of the variables are integers, and the equation is equal to a constant. The process involves simplifying and rearranging terms to achieve this standard form. In this case, we distributed the constants, simplified the expression, and rearranged the terms to meet the standard form criteria.