For the life of me I can't remember how to solve this all the way. I remember doing it but I can't think of it now. If someone would be so kind as to help me with these 2 problems and maybe explain how they did it, I would be very thankful!
Solve for x:
6x - 4/3 = 3/4x + 1/3
and
5(x+1) = 7x+3
2007-09-12 17:12:42 · 12 answers · asked by Vicki 3 in Science & Mathematics ➔ Mathematics
get your x's on one side, everything else on the other side. So add 4/3 to 1/3. That is 5/3. Move the 3/4x to the other side. You have to subtract since it is positive. So:
6x-3/4x=5/3
5 1/4 x= 5/3 make it into an improper fraction so you can divide.
21/4x=5/3
x= 5/3 *4/21 (cross multiply)
so 5*4=20 3*21=63
x=20/63
2007-09-12 17:19:48 · answer #1 · answered by niffer 3 · 0⤊ 0⤋
The easiest way to solve the first would be to get rid of the fractions. To do this, we'll need to multiply by the Least Common Multiple of the denominators of all of the fractions. Our denominators are 3, 4, and 3, so the LCM is 12. If you multiply the entire equation by 12, all of the fractions will disappear.
[6x - 4/3 = 3/4x + 1/3](12)
72x - 48/3 = 36/4x + 12/3
72x - 16 = 9x + 4
-9x -9x
63x - 16 = 4
+16 +16
63x = 20
x = 20/63
The only way this is wrong is if your 3/4x is actually 3/(4x), meaning the x is on the bottom. I assumed you meant (3/4)x, with the x either on top or right next to the fraction. If it is supposed to be on the bottom, then you need to multiply by 12x to get all of the fractions to cancel, and you'll get this:
[6x - 4/3 = 3/4x + 1/3](12x)
72x^2 - 16x = 9 + 4x
72x^2 - 20x - 9 = 0
This gets pretty nasty, so I'm guessing the first one is right.
5(x + 1) = 7x + 3
distribute the 5 to the x and the 1
5x + 5 = 7x + 3
-5x -5x
5 = 2x + 3
-3 -3
2 = 2x
1 = x
2007-09-12 17:26:02 · answer #2 · answered by cubs_woo_cubs_woo 3 · 0⤊ 0⤋
6x - 4/3 = (3/4)x + 1/3 original equation
6x - (3/4)x = 1/3 + 4/3 move all terms with x on one side
(24/4)x - (3/4)x = 1/3 + 4/3 find common denominators
(21/4)x = 5/3 simplify
63x = 20 multiply both sides by 12 to clear fractions
x = 20/63 divide both sides by 20
5(x+1) = 7x+3 original equation
5x + 5 = 7x + 3 distribute 5 and remove parentheses
5x - 7x = 3 -5 group x terms
-2x = -2 simplify
x = 1 solve
2007-09-12 17:23:00 · answer #3 · answered by tkquestion 7 · 0⤊ 0⤋
First, put both terms with an x on the left side. Subtracting 3/4 from 6, we get 5.25x - 4/3 = 1/3. Move the 4/3 to the right side, and you have 5.25x = 5/3. Divide both sides by 5.25, and you have x = 20/63.
First distribute, which gives you 5x+5=7x+3, then move x terms to the right and numbers to the left. You get 2x=2. Dividing by 2, you have x=1.
2007-09-12 17:27:43 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Vicky,
basically just isolate the x...
6x - 4/3 = 3/4x + 1/3
6x - 3/4x = 1/3 + 4/3
x(6 - 3/4) = 5/3
x = (5/3)/(6 - 3/4)
x = 0.3175
5(x+1) = 7x + 3
5x + 5 = 7x + 3
2 = 2x
1 = x
REgards,
Chas.
2007-09-12 17:20:18 · answer #5 · answered by Chas. 3 · 0⤊ 0⤋
6x - 4/3 = 3/4(x) + 1/3
+ 4/3
6x = 3/4(x) + 5/3
- 3/4(x)
5 1/4 (x) = 5/3
21/4(x) = 5/3
* 4/21
x = 5/3 * 4/21
x = 20/63
5(x + 1) = 7x + 3
5x + 5 = 7x + 3
-3
5x + 2 = 7x
- 5x
2 = 2x
/2
x = 1
2007-09-12 17:22:54 · answer #6 · answered by Anonymous · 0⤊ 0⤋
6x-4/3 = 3/4x + 1/3
need to get x on one side
6x-3/4x -4/3=1/3
move -4/3 to other side
6x-3/4x=4/3+1/3
simplify
5.25x=5/3
solve for x
x= 5/3 / 5.25
x= .317
5(x+1)=7x+3
distribute
5x+5=7x+3
x to one side
-2x+5=3
move 5 to the other side
-2x=-2
x=1
if you moved x to the right you would get 5=2x+3
2=2x
x=1
most people are used to keeping the variable on the left but i do know some that move theirs to the right. same answer! hope this helped.
2007-09-12 17:33:41 · answer #7 · answered by noelsluv 4 · 0⤊ 0⤋
First one, multiply the entire thing by the lowest common denominator to get rid of the fractions. So the lowest number that 3 and 4 go into evenly is 12. So multiply each term by 12 (or 12/1).
12*6x-12*4/3=12*3/4x+12*1/3
72x-16=9x+4 (multiply and reduce)
63x=20 (move all of your x's to one side by subtracting 9x from both sides, and all of your numbers (constants) to the other side by adding 16 to both sides)
x=20/63 (divide both sides by 63)
Second one, use the distributive property to clear the parentheses. Multiply the number on the outside of the parentheses by each number inside.
5x+5=7x+3
2=2x (subtract 5x from both sides to get x's all on one side and subtract 3 from both sides to get numbers on the other side of the = sign)
1=x (divide both sides by 2)
2007-09-12 17:26:34 · answer #8 · answered by Mada 2 · 0⤊ 0⤋
x= negative 20/7
and
x=1
2007-09-12 17:42:56 · answer #9 · answered by Amy 1 · 0⤊ 0⤋
for the first one its x=20/63
for the second its x=1
2007-09-12 17:24:10 · answer #10 · answered by flame_yoshi05 2 · 0⤊ 0⤋