Solve for x in each of the following:
a: 2/3x = 11/6
b: 3/4 / x = 1/3
c: 5/6 - 2/3x = 3/4
d: 2x/3 + 1/4 = x/6 - 1/2
Please help me and explain, I don't get fractions at all!
11/6= 6*1 +1=7/6
2x/3=7/6
2x*6=7*3
x=21/12=7/4
x=3/4*3=9/4
5/6-3/4=2/3x for 5/6-3/4---> 6*4=24 then
(5*4)/24-(3*6)/24=2/3x
(20-18)/24=2/3x
2/24=2/3x
x=1/8
You posted the same question yesterday as Rose .
Very confusing if you change names
http://www.jiskha.com/display.cgi?id=1413026488
I am mainly confused with problem D. I don't understand and have yet to get the right answer.
Sure! I can help you solve these equations involving fractions. Dealing with fractions can seem a bit tricky at first, but it's actually quite straightforward once you know the rules. Let's go through each equation step by step:
a: 2/3x = 11/6
To solve for x, we want to isolate x on one side of the equation. In this case, we want to get rid of the fraction on the left side. To do this, we can multiply both sides of the equation by the reciprocal of the coefficient of x, which in this case is 3/2.
2/3x * (3/2) = 11/6 * (3/2)
Simplifying both sides, we have:
1x = 33/12
Now, we can simplify the right side of the equation by dividing the numerator and denominator by their greatest common divisor, which is 3:
x = (33/3) / (12/3)
x = 11/4
b: 3/4 / x = 1/3
To solve for x in this equation, we will again aim to isolate x. In this case, x is in the denominator, so we can handle this by multiplying both sides by x.
(3/4) / x * x = (1/3) * x
Simplifying both sides, we have:
3/4 = x/3
To eliminate the fraction on the right side, we can multiply both sides by the reciprocal of 3/1, which is 1/3.
3/4 * (1/3) = (x/3) * (1/3)
Simplifying both sides, we get:
1/4 = x/9
To solve for x, we can cross-multiply:
4 * x = 1 * 9
4x = 9
Finally, dividing both sides by 4 gives us:
x = 9/4
c: 5/6 - 2/3x = 3/4
To solve for x in this equation, we want to combine like terms and isolate x. Let's first get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 12.
(5/6) * 12 - (2/3x) * 12 = (3/4) * 12
Simplifying both sides, we have:
10 - 8x = 9
Next, let's isolate x.
10 - 8x - 10 = 9 - 10
Simplifying further:
-8x = -1
To solve for x, divide both sides by -8:
x = -1 / -8
x = 1/8
d: 2x/3 + 1/4 = x/6 - 1/2
To solve for x in this equation, we want to combine like terms and isolate x. Let's get rid of the fractions first by multiplying both sides by the least common multiple (LCM) of the denominators, which is 12.
(2x/3) * 12 + (1/4) * 12 = (x/6) * 12 - (1/2) * 12
Simplifying both sides, we have:
8x + 3 = 2x - 6
To isolate x, we can move all terms with x on one side and all constant terms on the other side:
8x - 2x = -6 - 3
Simplifying further:
6x = -9
To solve for x, divide both sides by 6:
x = -9 / 6
x = -3/2
I hope this explanation helps! Let me know if you have any further questions.