trying to help son with math. 2j-5=8j+7(i got j=3) -22-3d=-2d+d-3d(i got lost) on -42+4c=-c+3c-c(i got c=-42)?

Question

on 8y+20=y+2y-5y (i got y=20) on 4b-10=b+3b-2b(i got b=5) on -7f+2f=-36+f+3f(i got f=-9) on -5a+7a=-18+3a+5a(i got a=-3) on 9y+2=3(y+4) (i got 14/6 but stuck)

Answer 1

2j-5=8j+7
-7-5 = 8j -2j
-12 = 6j
j = -2
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-22-3d=-2d+d-3d
-22= -2d+d-3d +3d
-22 = -d
d =22
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-42+4c=-c+3c-c
-42 = -c+3c-c-4c
-42 = -3c
c= 42/3 = 14
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last
9y+2=3(y+4)
9y+2=3y+12
9y-3y=12-2
6y=10
y=10/6 =5/3
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Answer 2

Hey Dad, you seem to be missing the technique that works for all these problems. The idea is this:

(1) By adding or subtracting the same quantity to both sides of the equation, you want to have all the terms involving the variable on one side, and all the constants on the other.

(2) Combine like terms on both sides.

(3) If the coefficient of the unknown is not 1, divide both sides by that coefficient.

For example, consider your first problem: 2j - 5 = 8j + 7. First we subtract 2j from both sides; we think 2j - 5 - 2j = 8j + 7 - 2j, but we write -5 = 8j + 7 - 2j. Next we subtract 7 from both sides; think -5 - 7 = 8j + 7 - 2j - 7, but simply write
-5 - 7 = 8j - 2j. Now combine like terms, and get -12 = 6j. Since the coefficient of j is 6, we divide both sides by 6 and get -12/6 = 6j/6 or -2 = j.

One more example: 8y + 20 = y + 2y - 5y. We first subtract 8y from both sides and get 20 = y + 2y - 5y - 8y. Combining like terms we get 20 = -10y. Dividing by -10 we get -2 = y.

I hope this helps. Good luck.

Answer 3

14/6 is correct...but finish it...put it in smaller terms and your answer is 7/3