Question

Given that 4(n-5)+2=3(n-1),what is the value of n

Answer 1

Okay, so we'd have to break down the equation and simplify it fully to find the value of n. Your equation is : 4(n - 5)+ 2 =3(n - 1)

Let's break down the left side of the equation first, by simplifying it and distributing. We would distribute the 4 to the numbers and variable inside the parentheses. That would make it : 4n - 20 + 2 = 3(n - 1)

Since we can simplify further on the left side by adding 2 to -20, we'll do just that. That would make : 4n - 18 = 3(n - 1)

There's nothing more to simplify on the left side, so we'll move on to the right side, by distributing the 3 outside the parentheses to the number and variable inside the parentheses. That would make it : 4n - 18 = 3n - 3

Now that both sides are fully simplified, we add like terms together. 18 is the first number to catch my eye, so we'll add 18 to both sides. This would cross out the 18 on the left, and add 18 to -3. That would make the equation :

4n = 3n + 15 : (since -3 plus 18 make 15.) Now, the last pair of like terms include coefficients, so we'll subtract 3n to both sides. That would get rid of 3n on the right, and subtract 3n to the left. That would make it : n = 15

Answer 2

We'll first simplify both sides of the expression to get (simply using the distributive property):

`4n-20+2=3n-3`

Then, we can simplify a little bit:

`4n-18 = 3n-3`

To solve for n, we have to isolate it. Let's subtract 3n from both sides to further simplify it:

`n-18 = -3`

Then, add 18 to both sides to get the value of n:

`n = 15`

And that's your answer. If you have questions on how I got that, feel free to ask!