-40+5n=-3(8-3n)

Question

What is n?

 

Answer 1

1. Dania,  I'll set the problem up and do a check for correct answer.   -40n+5n=-3(8-3n)=  -40+5n=-24+9n= -40=-24+4n= -16=4n= n= -4.   Check:  -40+5(-4)= -3(8-3(-4)= -40-20=-24-36= -60=-60

Answer 2

Okay Dania, remember we need to isolate the variable, n. Let's begin on the right side of the equation:

-3(8-3n), because we should distribute it out to get rid of the parentheses. So, -3 times 8 is -24, and -3 times -3n is 9n. So now we have -40+5n=-24+9n. Now, let's move the variable 9n from the right side of equation to the left. Then we have -40+5n-9n=-24. Remember when we move a 9n to the other side of the equation, we have to change its value to negative. Now let's move the -40 to the right side of the equation, again changing its value, this time to 40. Thus we have 5n-9n=-24+40.

 

First, we calculate the left side, giving us -4n, and then the right, 40-24, giving us 16. Therefore, we have -4n=16. We can express it this way:

-4n=16

-4.   -4

 

Divide both sides by -4 and you find the variable as n=-4

Answer 3

For this question, you want to eliminate the parentheses and have n on just one side of the equation so n equals a number value.

 

First, let's remove the parentheses. Because there is a -3 in front of (8-3n), the three must be multiplied by every term inside the parentheses. The negative sign from -3 changes the minus sign between 8 and 3n, so it becomes an addition sign: -3(8-3n)= -3•8–(-3)•3n which is -24+9n.

 

Now the equation is -40+5n= -24+9n. Notice how n appears on both sides of the equation. You want to isolate n so it can be solved, so you do what is called combine like terms (grouping terms together that have the same "tag"). In this case, 5n and 9n are like terms, so one of them can be "moved" to the other side of the equal sign. It's a little easier to keep terms positive, so let's combine 5n with 9n by taking 5n away from both sides: -40+5n -5n= -24 +9n -5n which is -40= -24 +4n.

 

Doing the same for the numbers since numbers can be grouped together, combine -24 to -40 by adding 24 to both sides so it leaves 4n isolated: -40 +24= -24 +24 +4n.

 

Now the equation is -16=4n. Here, we want to isolate n, so we must remove the coefficient (the number in front of the variable, here it's 4) by dividing from both sides: -16 /4= 4n/4.

 

This leaves us with n= -4. It's a good idea to check to see if it works, but be careful with the negative signs!: -40+5(-4)= -3[8-(3•-4)] which is -40+ -20=-3(8- -12) or -60= -3(20).

 

Does -60=-60? YES so n= -4