How would I solve the multi step equation...2/3( x+7) - 3x = 1/2( 2x - 7) - 1/6?

Question

Please be pacific with how to cancel out the fractions but also with solving the problem

Answer 1

Since the common denominators are 6, multiply both sides by 6:
6(2/3(x+7)-3x)=6(1/2(2x-7)-1/6)
4(x+7)-18x=3(2x-7)-1

Distributive Property:
4x+28-18x=6x-21-1

Combine Like Terms:
-14x+28=6x-22

Subtract 6x on both sides:
-20x+28=-22

Subtract 28 on both sides:
-20x=-50

Solve:
x=-50/-20=5/2 or 2.5

Check:
-20(5/2)+28=-22
-50+28=-22
-22=-22

I hope this helps!

Answer 2

You first clear parentheses. Then you combine like terms. Then you get the variables on one side, and the numbers on the other side Then you divide both sides by the number in front of the variable. 6 + 4(x - 2) = x + 7 : original 6 + 4x - 8 = x + 7 : clear parentheses 4x - 2 = x + 7 : combine like terms 3x = 9 : x on left, numbers on right x = 3 : divide by 3, the number in front of the x 3x + 5 = 2x + 7 x = 2 <-- subtract 2x from both sides, then 5 from both sides 5(x - 3) + 2 = 3(x + 1) 5x - 15 + 2 = 3x + 3 5x - 13 = 3x + 3 2x = 16 x = 8

Answer 3

Actually, you want me to be "specific". Being pacific would probably mean solving this in a peaceful manner, but I can do that too.

First, get rid of the troublesome fractions. Your denominators are 2, 3 and 6. If you multiply your equation by the least common multiple of these three, you will not have any more fractions. 6 is divisible by both 2 and 3, so multiplying by 6 will do the job.

You get 6*(2/3)*(x+7) - 6*3x = 6*(1/2)*(2x-7) - 6*(1/6)
which becomes
4(x+7) - 18x = 3(2x-7) - 1.

Now, multiply everything out, using the distributive law:
4*x + 4*7 - 18x = 3*2x - 3*7 - 1
becomes
4x + 28 - 18x = 6x - 21 - 1.

Then, combine like terms:
(4x-18x) + 28 = 6x - (21+1)
becomes
-14x + 28 = 6x - 22.

Rearrange so that all terms involving x are on one side, and all other terms are on the other side:
28 + 22 = 6x + 14x
Combine like terms again:
50 = 20x

so x = 50/20 = 5/2.

Answer 4

Multiply everything out, so that you have no more brackets.

2x/3 + 14/3 -3x = x - 7/2 - 1/6

Group the x terms and the other terms. Find the common denominator for each and add them out.

2x/3 - 3x - x = -7/2 - 1/6 -14/3

(2x -9x - 3x)/3 = (-21 -1 - 28)/6

-10x/3 = -50/6

Get the denominators to the other side of the equation, multiplying:

6(-10x) = 3(-50)

-60x = -150

x = -150/-60

x = 2.5

Answer 5

The answer is 5/2 or 2.5

you can use any of the methods that got that for an answer. I multiplied both sides by six to get rid of the fractions first.

Answer 6

Sorry, the question you type is ambiguous as in I am not sure if the fraction is placed outside the parenthesis or if the parenthesis is placed as the denominator, but I'll try to answer it using the first interpretation.

⅔(x+7) - 3x = ½(2x-7) - 1/6

Step 1: Multiply what's in the parenthesis with the numerator.
(2x+14)/3 - 3x = (2x-7)/2 - 1/6

Step 2: Change to same denominator for the right side.
(2x+14)/3 - 3x = (6x-21)/6-1/6

Step 3: Add the right side.
(2x+14)/3 - 3x = (6x-21-1)/6
(2x+14)/3 - 3x = (6x-22)/6

Step 4: Change to same denominator for the left side.
(2x+14)/3 - 9x/3 = (6x-22)/6

Step 5: Add the left side.
(2x+14-9x)/3 = (6x-22)/6
(14-7x)/3 = (6x-22)/6

Step 6: Cross multiply (that's just one way).
6(14-7x)=3(6x-22)
84-42x=18x-66

Step 7: Group x on the right side and the numbers on the left.
84+66=18x+42x
150=60x
x=150/60
x=2.5

Answer 7

You can see that if we multiply thruout by 6, fractions will disappear.Let us do that:
4(x+7)-18x=3(2x-7)-1...(2).Now , get rid of the brackets:
4x+28-18x=6x-21-1
or
-14x+28=6x-22.
x on one side:
-20x=-50.
Cancel -ve/simplify
x=2.5.
ALWAYSinsert the answer back into the original eq and check.

Answer 8

how easy :
2X/3+14/3-3X=2/2X-7/2 - 1/6
4X/6+28/6-18X/6=6X/6-21/6-1/6
4X+28-18X=6X-21-1
4X-6X=-21-1-28+18
-2X=-32
2X=32
X=32/2
X=16 this is the solution of the equation

Answer 9

2/3x+2/3into7-3x=1/2into2x-1/2into7-1/6: x=5

Answer 10

multiply the whole equation by 6, because it is their LCD.

6(2/3(x-7)-3x=1/2(2x-7)-1/6)

4(6x-42)-18x=3(12x-42)-1

24x-168-18x=36x-126-1

6x-168=36x-127

6x-36x=-127+168

-30x=41

x= -41/30