Solving Linear Equations?

looks like you need to solve these for x or y which ever is in each problem.
linear equations are usually graphing problems and have a y and an x

maybe you just graph x or y

If that is what you want then when you have an x you would graph a vertical line

when you have a y you would graph a horizontal line

I explained how to solve these, make sure you need to graph them before you do.

1) 1/2 (x-3) = 1/3 (2x+1)
multiply by distributing
get x on one side numbers on the other side

2) 1/2 x = 40
mul by 2 to clear fraction
done

3) 1/4 (3x - 5) = 2x + 3
mul by 4 to clear fraction
get x on one side numbers on other side

4) 3y + 1/2 = 4 + 2/3 y
mul by 6 common denominator
get y on one side
numbers on the other side

hope this helps!!!

It is important that brackets be used to avoid misunderstanding:-

Question 1
(1/2)(x - 3) = (1/3) (2x + 1)
3(x - 3) = 2(2x + 1)
3x - 9 = 4x + 2
- 11 = x
x = - 11

Question 2
(1/2) x = 40
x = 80

Question 3
(1/4) (3x - 5) = 2x + 3
3x - 5 = 8x + 12
- 17 = 5x
x = - 17/5

Question 4
Reading this as :-
3y + 1/2 = 4 + (2/3) y
18y + 3 = 24 + 4y
14y = 21
y = 3/2

1st question:
1/2(x - 3) = 1/3(2x + 1)
3(x - 3) = 2(2x + 1)
3x - 9 = 4x + 4
x = 13

2nd question:
1/2x = 40
x = 80

3rd question:
1/4(3x - 5) = 2x + 3
3x - 5 = 8x + 12
5x = 17
x = 17/5

4th question:
3y + 1/2 = 4 + 2/3y
18y + 3 = 24 + 4y
14y = 21
2y = 3
y = 3/2

1/2 (x-3) = 1/3 (2x+1)
3(x-3) = 2(2x+1) ---> Whole equataion multiplied by 6 to remove fractions
3x - 9 = 4x + 2 ---> Distribute
3x - 4x = 2 + 9 ---> Bring 4x to the left side and 9 to the right
-x = 11
x = -11 ---> Multiply the whole equation by (-1) to find x

1/2 x = 40
x = 80 ---> Multiply the whole equation by 2 to remove fraction

1/4 (3x - 5) = 2x + 3
3x - 5 = 4(2x + 3) ---> Multiply the whole equation by 4 to remove fraction
3x - 5 = 8x + 12 ---> Distribute
3x - 8x = 12 + 5 ---> Bring 8x to the left side and 12 to the right
-5x = 17
-x = 17/5 ---> Divide to find -x
x = -17/5 ---> Multiply the whole equation by (-1) to find x

3y + 1/2 = 4 + 2/3
18y + 3 = 24 + 4y ---> Multiply the whole equation by 6 to remove fraction
18y - 4y = 24 - 3 ---> Bring 4y to the left side and 3 to the right
14y = 21
y = 21/14 ---> Divide the whole equation by 14 to find y
y = 3/2 ---> Leave your answer in a simplified form

1)
(1/2)(x - 3) = (1/3)(2x + 1)
(x - 3)/2 = (2x + 1)/3
3(x - 3) = 2(2x + 1) (cross multiply)
3x - 9 = 4x + 2
3x - 4x = 9 + 2
-x = 11
x = 11/-1
x = -11

2)
(1/2)(x) = 40
x/2 = 40
x = 2(40)
x = 80

3)
(1/4)(3x - 5) = 2x + 3
(3x - 5)/4 = 2x + 3
3x - 5 = 4(2x + 3)
3x - 5 = 8x + 12
3x - 8x = 5 + 12
-5x = 17
x = -17/5 (-3.4)

4)
3y + 1/2 = 4 + (2/3)(y)
3y + 1/2 = 4 + 2y/3
6(3y + 1/2) = 6(4 + 2y/3)
18y + 3 = 24 + 4y
18y - 4y = 24 - 3
14y = 21
y = 21/14
y = 3/2 (1.5)

1) 1/2x - 3/2 = 2/3x + 1/3 (just multiply)
1/2x - 2/3x = 1/3 + 3/2 (shift)
3x-4x/6 = 2+9/6 (LCM)
-1x/6 = 11/6
-1x = 11 (cancelling 6 on both sides)
x = -11

2) 1/2x = 40
1x = 40 X 2
x = 80


3) 1/4 (3x-5) = 2x+3
(3x-5) = 4(2x+3) (take 1/4 to the oder side)
3x-5 = 8x + 12
3x-8x = 12+5
-5x = 17
x = -17/5


4) 3y + 1/2 = 4 + 2/3y
3y - 2y/3 = 4 - 1/2
9y-2y/3 = 8-1/2
7y/3 = 7/2
y = 7X3 / 7X2 (shift 7 and 3 to the oder side)
y = 21/ 14
y = 3/2



hey, jun's 1st answer is wrong
2( 2x+1) is 4x + 2 and not 4x + 4

the basic formula of a linear equation is y = mx + c.
u need to convert it to this
for example the second equation would be
y = 1/2x + 40
then work at either x or y depending on which one ur trying to find out
y is the vertical luine, and x is the horizontal line.