Final answer:
To put the equation 3(x-6)=4(v-8) in standard form, distribute the 3 and 4, rearrange the equation to get 3x = 4v - 14, and then write it as 3x - 4v = -14.
Step-by-step explanation:
To write the equation 3(x-6)=4(v-8) in standard form, we must distribute the numbers outside the parentheses and then rearrange the equation, if necessary so that it is in the form Ax + By = C. First, we will distribute the 3 to both x and -6, which gives us 3x - 18. Similarly, we distribute the 4 to v and -8, resulting in 4v - 32. Now, the equation looks like this:
3x - 18 = 4v - 32
Since we need it in standard form, we need to get the variables on one side and the constants on the other side. To do this, we can add 18 to both sides to move the constant to the right side:
3x = 4v - 32 + 18
Which simplifies to:
3x = 4v - 14
Now the equation is in the desired standard form 3x - 4v = -14.