-67 = -8n + 5. –Problem 1

-67 – 5 = -8n + 5 – 5 Subtract 5 from both sides

-72 = -8n –Simplified

-72 / -8 = -8/-8n –Divide by -8 on both sides

9 = n –Solution

Problem 2 will be solved in a similar manner:

k/3 – 19 = -26

k/3 – 19 + 19 = -26 + 19

k/3 = -7

3*k/3 = -7*3

k = -21

Just remember for these problems, when you add to one side, you need to subtract from the other to make the equation stay true. Likewise, if you divide from one side, you need to multiply on the otherside the same amount. If you multiply one side, you need to divide the other, and if you subtract from one side, you need to add to the other, the same amount.

Hope this helps. 🙂

So, let’s do the first step. Let’s get rid of the 5 on the right-hand side. Subtract five from each side. -67-5= -8n + 5-5 becomes, then, -72=-8n, correct? Then, to further isolate the “n” we must divide each side by

-8. So, -72 divided by -8= -8n divided by -8, or 9=n.Thus, 9 =n. The answer is 9. To make sure we’re right, put 9 back into the original equation. -67=-8 X 9 +5, or -67=

-72 + 5 , or -67=-67. So, we’re correct.

The same idea applies to the second problem. We must isolate the variable, in this case, the “k.” The first step, then, is to add 19 to both sides. k/3-19 +19=-26 + 19. Thus, k/3=-7. Then, we have to multiply by 3 to further isolate the k. k/3 X 3= -7 x3. Thus, k=-21. To see if we’re right, put -21 back in the equation. -21/3-19=-26. Is this true? Let’s see. -7-19=-26. So, we’re correct!

First for:

-67= -8n+5

The first thing you do is simplify the equation. So, you subtract 5 from both sides:

-67(-5)= -8n+5 (-5)

So the 5’s cancel out on the right hand side. And you end up with:

-67 -5 = -8n

By simplifying the equation again you end up with:

-72 = -8n

The next step is to isolate the n. So, the next thing you need to do is divide by -8. So you end up with:

-72 = -8n

—– —–

-8 -8

The -8’s cancel out on the right hand side and you are left with:

-72 = n

——

-8

Since they are both negative numbers, the negative symbols cancel each other out and you end up with:

72 = n

—-

8

By simplifying again you end up with:

9 = n

To make sure this is the solution, you go back and verify it with the original equation. So, you plug 9 into the spot where the n was.

So, you have:

-67= -8 x (9) +5

You end up with:

-67= -72 +5.

Which equals:

-67 = -67.

So, since both sides are equal, the solution N=9 is correct.

As far as the second equation:

k -19 = -26

—

3

The first step is to isolate the k, so you add 19 to both sides:

k – 19 = -26

— +19 +19

3

So, the -19 and the +19 cancel each other out on the left hand side of the equation and you end up with:

k = -26 +19

—

3

By simplifying again you end up with:

k = -7

—

3

Then to completely isolate the k, you need to multiply both sides by 3. So you end up with:

3k = -7 x 3

—-

3

So, the 3’s cancel each other out on the left part of the equation and you end up with:

k = -7 x 3

Which equals:

k = -21

So, to verify that’s right. . . you plug -21 into the equation in place of the k. Which means you end up with:

(-21) -19 = -26

——-

3

Which equals:

-7 -19 = -26

Which equals:

-26 = -26

So, the solution k = -21 is correct. Does that make sense? Hopefully this helps; let me know if you need more help.

The trick here is to use what I like to call the gift-wrapping method. When you give a gift, you put the gift in a box, you wrap the box in wrapping paper, and then you but ribbon around the wrapping paper. Does the recipient of your gift un-do these changes in the same order? Does one open the box, then tear the paper, then cut the ribbon? No – changes must be un-done in the opposite order in which they were made. The same is true in Math.

Look at the ‘n’ in the first equation. There are two “changes” being made – a multiplication of (-8), and an addition of 5. Remember to think of operations, not values. The values, -8 and 5, are almost irrelevant. The important idea here is that, according to the order of operations, the multiplication happened first (box), then the addition (wrapping paper).

Start by tearing the wrapping paper; subtract 5 from both sides. { -72 = -8n }

Now, open the box. Divide both sides by -8, and see that n = 9.

The second equation is essentially the same, so I leave it to you for practice. I hope this helps! 🙂

The second problem you start out the same way you add 19 to both sides giving you k/3 = -7. Then you will multiply each side by 3 giving you k=-21.

Hope that this helps you.

67+5=8n

72/9=8

-67-5=-8n

-72=-8n

72=8n

72/8=n

9=n

Proof:

-67=(-8*9)+5

-67=-72+5

-67=-67

Try the same method for number 2

Good luck

8n=72

n=9

k/3-19+19=19-26

k/3=-7

k=7/3 or 2 1/3

subtract five from both sides (-72 = -8n)

and divide by negative eight (9 = n)

question two:

add nineteen to both sides (k/3 = -7)

and multiply by 3 (k = -21)