2/3(4x - 1) - (4x- 1-3x/2)= x-7/2. Find the value of x ?
To find the value of x, we need to simplify the equation step by step. Let's start by expanding the equation:
2/3(4x - 1) - (4x - 1 - 3x/2) = x - 7/2
First, simplify both sides of the equation:
(8/3)x - 2/3 - (4x - 1 - 3x/2) = x - 7/2
Next, simplify the expression inside the parentheses on the left side:
(8/3)x - 2/3 - (4x - 1) + 3x/2 = x - 7/2
Distribute the 2/3 to both terms inside the first parentheses:
(8/3)x - 2/3 - 4x + 1 + 3x/2 = x - 7/2
Combine like terms on the left side:
(8/3)x - 4x + 1 + 3x/2 = x - 7/2
Now, simplify the right side by finding a common denominator for both fractions:
(8/3)x - 4x + 1 + (6/2)x/2 - 7/2 = x - 7/2
(8/3)x - 4x + 1 + (3/2)x - 7/2 = x - 7/2
Now, combine like terms on both sides:
(8/3)x - 4x + (3/2)x - 7/2 = x - 7/2
Find the least common denominator of all the fractions involved, which is 6:
[(16/6)x - (24/6)x + (9/6)x - (21/6)] = [(6/6)x - (42/6)]
Combine like terms on both sides:
(-14/6)x - (12/6) = (-36/6)x - (42/6)
Simplify both sides:
(-7/3)x - 2/3 = (-6)x - 7
Multiply both sides of the equation by -3 to eliminate the fraction:
(-3)(-7/3)x - (3)(2/3) = (-3)(-6)x - (3)(7)
Simplify both sides:
7x + 2 = 18x + 21
Now, move all the terms with x to one side of the equation:
7x - 18x = 21 - 2
Combine like terms:
-11x = 19
Finally, divide both sides by -11 to solve for x:
x = 19/-11
Thus, the value of x is approximately -1.727 (rounded to three decimal places).
as written
2/3(4x - 1) - (4x- 1-3x/2)= x-7/2
x = 23/5
If you meant
2/3 * (4x - 1) - (4x - (1-3x)/2)= x - 7/2
x = 20/23
If some other parenetheses were intended, then some other answer will result