Solving equations with variables on both sides.?

Question

can someone tell me how to do problems like . . .

1.-3g + 9 = 15g - 9

2.4x + 27 = 3x + 34

3.10y = 2y - 6y + 7

4. 4 + 6x - 9x = 3x

5.13x + 8 + 8x = -9x - 22

6.5x - 3x + 4 = 3x + 8

these are so hard i have no clue what to do.

Answer 1

Use the simple rule that whatever you do to one side of an equation you have to do to the otherside to ensure that the nature doesn't change. Below is the answer to the first equation that you have, I have given you all the steps required to find the answer.

1. -3g + 9 = 15g - 9
3g - 3g + 9 = 15g - 9 + 3g
0 + 9 = 18g - 9
9 + 9 = 18g - 9 + 9
18 = 18g + 0
18/18 = 18g / 18
1 = g

I hope that this helps you find the answer to the remaining questions, if you still need feel free to contact me.

Good luck

Answer 2

Your goal is to simplify the equations so that the unknown appears on one side with constants on the other.

You do this by performing "safe" operations such as adding or subtracting the same value to both sides of the equation.

For example:

if x = 10, then it is also true that
x + 5 = 10 + 5 and
x + x = 10 + x

So let's start with equation #1:
-3g + 9 = 15g - 9

Looking at the "-9", let's add 9 to both sides:
-3g + 9 + 9 = 15g - 9 + 9

Doing the arithmetic on the two sides:
-3g + 18 = 15g

Looking at the "-3g", let's add "3g" to both sides:
-3g + 18 + 3g = 15g + 3g

Since we care allowed to rearrange under addition (2 apples plus 3 oranges is the same as 3 oranges + 2 apples), we get:

-3g + 3g + 18 = 15g + 3g

Combining the coefficients of the "g" terms (2 apples plus 3 apples is 5 apples):

(-3 + 3)g + 18 = (15 + 3)g
0g + 18 = 18g

Zero times anything is zero so:
0g + 18 = 0 + 18 = 18 so we have
18 = 18g

Divide both sides by 18 to get:
1 = g

Now we check:

(-3)(1) + 9 vs. 15(1) - 9
(-3) + 9 vs 15 - 9
6 vs. 6 - check

Answer 3

Try to get the variable on one side and the numbers on the other...

e.g. 4 + 6x - 9x = 3x
add 9x to both sides and you get
4 + 6x = 3x + 9x
take 6x away from both sides and you get
4 = 3x + 9x - 6x

now, since 3+9-6 = 6 we can also say
4 = 6x

again, get the numbers on one side only, so divide by 6
4/6 = x = 2/3 (or 0.6666666666666...)

prove the equation by substituting the value of x
4 + 6(2/3) -9(2/3) = 3(2/3)
4 + 4 - 6 = 2

QED

Answer 4

Bring all the variables to left side and then solve

Ex:
1)

-3g + 9 = 15g - 9

bring 15g from right to left by subtracting 15g from both sides

-3g - 15g + 9 = -9

subtract 9

-18g = -18

g = 18/18 = 1

now you can complete all the remaining in the same fashion

Answer 5

You can add multiples of the variable to both sides in exactly the same way as you would add a number to each side. Same goes for multiplying or dividing by a variable too, but you don't need to do that with these examples.

Take equation 2 as an example.
4x + 27 = 3x + 34
Subtract 27 from both sides:
4x + 27 - 27 = 3x + 34 - 27
So 4x = 3x + 7
Now subtract 3x from both sides:
4x - 3x = 3x + 7 - 3x

But 4x -3x is x, and 3x - 3x is 0.
So we have x = 7.

The others are very similar.

Answer 6

ok, do it one step-at-time and you will locate that t = + a million: (a million) Algebraically upload "like" words: 9 - 6 = 3 and -t - t = -2t (2) So, on the left-section, you have: 3 - 2t and on the remarkable you nevertheless have t (3) Now, upload 2t to the two sides and you at the instant have: 3 = 3t, because of the fact -2t + 2t = 0 (on the left section) on a similar time as t + 2t = 3t (on the remarkable section) (4) finally, divide the two sides via 3 and you at the instant have a million = t or (what's the comparable ingredient) t = a million. be conscious: in case you are able to cope with elementary math, you shouldn't get right into a tangle. and don't be intimidated via "variables"; in elementary algebra, geometry, trig, etc. they are merely symbols that frequently designate numbers!!! additionally, you're able to get used to the "shorthand", alongside with (interior the above): 2t means "2 extra advantageous via t", and -2t means "minus a million extra advantageous via 2 extra advantageous via t", and the expression -2t + 2t = 0 means that "that sum is often 0, no remember the fee of t", etc. take exhilaration in!!!!

Answer 7

add/ subrract "VARIABLES" to get to one side....use the larger variable's side to go to ...

-3g +9 = 15g -9
(+3g) +9 (+9) = 15g (+3g) (+9)
18 = 18g .....g=1

Answer 8

You just have to bring the variables to one side (eg. left or right) and bring the numbers to the other side separately from the variables itself. Then you could solve the problems. It's easy, give it a try.