solve.
4x+2/3
-
3/4
= 1/2
4x + 2/3 - 3/4 = 1/2
multiply each term by 12 (I really don't like fractions)
48x + 8 - 9 = 6
48x = 7
x = 7/48
check:
left side = 28/48 + 2/3 - 3/4
= 7/12 + 8/12 - 9/12
= 6/12
= 1/2
= Right Side, Yeah!
4x +2/3-3/4 =1/2
or, when you combine 2/3 and -3/4,
4x-1/12=1/2
It's saying that you get 1/2 if you multiply a certain number by 4, then subtract 1/12 from it. You want to find the number itself, so peel away all of the operations you performed on it:
ADD BACK THE 1/12:
4x=7/12
DIVIDE OUT THE 4 (you just want x by itself, not 4 times x)
x = 7/48
You can verify that this is in fact that number that gives a value of 1/2 when you multiply it by 4 and subtract 1/12.
To solve the equation:
(4x + 2/3) / (3/4) = 1/2
We can start by simplifying the expression on the left-hand side of the equation.
First, let's simplify the fraction (2/3)/(3/4).
To divide fractions, we need to multiply the numerator by the reciprocal of the denominator.
2/3 divided by 3/4 is the same as 2/3 multiplied by 4/3:
(2/3) * (4/3) = 8/9
Now our equation becomes:
(4x + 8/9) = 1/2
Next, let's isolate x by subtracting 8/9 from both sides of the equation:
(4x + 8/9) - 8/9 = 1/2 - 8/9
Simplifying both sides of the equation gives:
4x = 9/18 - 16/18
Combining the fractions on the right-hand side gives:
4x = -7/18
To solve for x, we need to divide both sides of the equation by 4:
x = (-7/18) / 4
Dividing fractions is the same as multiplying the numerator by the reciprocal of the denominator:
x = (-7/18) * (1/4)
Simplifying the expression gives:
x = -7/72
Therefore, the solution to the equation is x = -7/72.