im helping my son and i am not sure I am right. 3d-8=-6+d (I got d=7) on 4-7m=m+4 (i got m=1)?

Question

on 4-9ju=j+4 (I got j=1 )on 6n-4n+20 (i got n=2)on 11e=9e+14 (i got e=7) on 5d-4=2d+6(i got it wrong) on 2j-5=8j+7(i got wrong also) these are hard for me to explain to my son.

Answer 1

3d-8=-6+d
2d=2
d=1

4-7m=m+4
4-8m=4
-8m=0

m=0

4-9j=j+4
-10j=0
j=0

6n-4n+20 *This is not an equation, only an expression, and can only be simplified to 2n+20.

11e=9e+14
2e=14
e=7

5d-4=2d+6
3d=10
d=10/3=3.33...


2j-5=8j+7
6j=-12
j=-2

Answer 2

3d-8 = -6+d
2d = 2
d=1

4-7m = m+4
0 = 8m
m=0

4-9j = j+4
0= 8j
j=0

6n - 4n =20
2n =20
n=10

11e = 9e +14
2e=14
e=7

5d-4 = 2d+6
3d=10
d=3.33333333

2j-5 = 8j+7
-6j = 12
j= -2

Answer 3

Here's the rule: you can do anything to an equation as long as you do it to both sides.

For example, x=1. With this I can say any of the following:

x + 1 = 1 + 1
x + y = 1 + y
2 * x = 2 * 1
and so on...

Your equations just require doing something to both sides that gets rid of all the bulky mess. So here is a STEP BY STEP process of doing all of it.

1.)
===================================
3d - 8 = -6 + d (subtract d from both sides)
-d..............- d
------------------
2d - 8 = -6 (add 8 to both sides)
..... +8... +8
------------------
2d = 2 (divide both sides by 2)
/2 ../2
------------------
d = 1

2.)
===================================
4 - 7m = m + 4 (subtract m from both sides)
.....-m ...- m
------------------
4 - 8m = 4 (subtract 4 from both sides)
-4......... -4
------------------
-8m = 0 (divide both sides by -8)
/-8 ../-8
------------------
m = 0

3.)
===================================
4 - 9j = j + 4 (subtract j from both sides)
.....-j....-j
------------------
4 - 10j = 4 (subtract 4 from both sides)
-4........ -4
------------------
-10j = 0 (divide both sides by -10)
/-10 ../-10
------------------
j = 0

4.) I'm going to assume that you meant 6n - 4n = 20
===================================
6n - 4n = 20 (subtract 4n from 6n)
------------------
2n = 20 (divide both sides by 2)
/2 .../2
------------------
n = 10

5.)
===================================
11e = 9e - 14 (subtract 9e from both sides)
-9e.....-9e
------------------
2e = -14 (divide both sides by 2)
/2 ..../2
------------------
e = -7

1.)
===================================
5d - 4 = 2d + 6 (subtract 2d from both sides)
-2d.......-2d
------------------
3d - 4 = 6 (add 4 to both sides)
..... +4..+4
------------------
3d = 10 (divide both sides by 2)
/3 ../3
------------------
d = 10/3 or 3.333333... or 3 1/3

6.)
===================================
2j - 5 = 8j + 7 (subtract 8j from both sides)
-8j......- 8j
------------------
-6j - 5 = 7 (add 5 to both sides)
.....+5... +5
------------------
-6j = 12 (divide both sides by -6)
/-6 ../-6
------------------
j = -2

Answer 4

3d-8=-6+d, by side change will give d=1
4-7m=m+4 will give m=0 (constant 4 is equal on both sides)
4-9ju=j+4 will give j= 0 if u is any non-zero value or j is any non-zero if u is 0
6n-4n+20 will give n= -10
5d-4=2d+6 will give d=10/3
2j -5=8j + 7 will give j=-2

Side change and simply will solve everything.

Answer 5

Close but no cigar. What you need to explain is when you add,or subtract on one side of the equation, you have to do the same on the other side of the equation.

If 3d - 8 = -6 + d, the first step is to get the variable term on one side and the constants on the other side. We do this by adding 8 to both sides and subtracting d from both sides. Then
2d = 2 and d=1.

If 4-7m= m+4, we subtract 4 from both sides and subtract m from both sides. Then -8m=0 and m=0.

Answer 6

3d - 8 = - 6+d
in steps
3d - 8 + 8 = - 6 + d + 8
3d = d = 2
3d - d = d + 2 - d
2d = 2
d = 1

4-7m=m+4 in steps
4 - 7m - m = m + 4 - m
4 - 8m = 4
4 - 8m - 4 = 4 - 4
- 8m = 0
m = 0

Answer 7

5d-4=2d+6
3d=10
d=3/10

2j-5=8j+7
6j=-12
j=-2

4-7m=m+4
8m=0
m=0


To explain it, you just have to group the variables on one side, and the constants on the other and solve for d (or whatever variable)

There really isn't any other way to explain it haha.

Answer 8

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Answer 9

3d-8=-6+d
2d=2
d=1

4-7m=m+4
8m=0
m=0

4-9j=j+4
8j=0
j=0

6n-4n+20=0
2n=-20
n=Negative 10

11e=9e+14
2e=14
e=7
5d-4=2d+6
3d=10
d=10/3

2j-5=8j+7
negative 12=6j
j=negative2

Answer 10

3d-8=-6+d
2d=2
d=1

4-7m=m+4
8m=0
m=0

2j-5=8j+7
6j=-12
j=-2